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Kui Wang

Publications and source records attributed to Kui Wang.

At least 19 recordsLinked to original sources
arXiv2026

Rigidity of Einstein Manifolds under Two Eigenvalue Conditions on the Curvature Operator of the Second Kind

We prove a rigidity theorem for closed Einstein manifolds of dimension $n\ge6$ under two lower bounds on the curvature operator of the second kind. More precisely, for $L_1, L_2\ge0$ and some real number $α>1$ in a suitable range, we consider \[ λ_1\ge-L_1\barλ, \qquad \frac1α\sum_{j=1}^αλ_j \ge-L_2\barλ. \] Here $λ_1\le\cdots\leλ_N$ are the eigenvalues of the curvature operator of the second kind $\mathring R$, $N=(n-1)(n+2)/2$, and $\barλ=N^{-1}\sum_{j=1}^Nλ_j$. Let $θ(n, α)$ be the constant appearing in \cite[Theorem~1.1]{CW26}; see (2). In the parameter range considered here, $L_2>θ(n, α)$, so the second condition is strictly weaker than the corresponding condition in \cite{CW26}, while the first condition and that condition do not imply each other. Under an additional explicit relation between $L_1$ and $L_2$, we prove that the manifold is either flat or a spherical space form.

math.DG↗
arXiv2026

The Faber-Krahn inequality for $p$-Hermite operators

We prove a Faber-Krahn inequality for the first eigenvalue of the $p$-Hermite operator (the weighted $p$-Laplacian with Gaussian weight) on Lipschitz domains in $\R^n$ under Robin boundary conditions with positive Robin parameter. The main result states that, among all domains of given Gaussian measure, the first eigenvalue is minimized by a half-space, and equality holds only for half-spaces. This extends the classical Faber-Krahn inequalities for the $p$-Laplacian \cite{BucurCV} to the $p$-Hermite operator and generalizes the linear case \cite{ChiacchioMathann} to the full nonlinear regime $p>1$.

math.SP↗
arXiv2026

How Roadside Units Enhance Intersection Safety? Cooperative Autonomous Driving System Design and A Proof of Concept

Intersections remain one of the most hazardous locations in urban road networks, where heterogeneous traffic participants and limited visibility frequently lead to severe traffic conflicts. In this paper, a vehicle-to-infrastructure-to-vehicle (V2I2V) cooperative system is proposed for improving road safety and traffic efficiency by using digital twins (DTs) deployed on roadside units (RSUs) to eliminate blind spots and centrally coordinate connected and automated vehicles (CAVs) in smart intersections. The proposed system integrates cloud-based global DTs for macroscopic guidance and RSU-based local DTs for real-time operations. Within this architecture, a hierarchical reinforcement learning (HRL) framework combines offline pre-training with online fine-tuning to achieve robust cooperative control. Experimental results show that the proposed system achieves substantial improvements in safety and efficiency in simulation experiments and real-world proof-of-concept (PoC) trials. In simulations, our system ensures high safety, efficiency, and smoothness under realistic communications and traffic constraints. In PoC trials, the RSU-centric control loop achieves a decision-making latency of approximately 42 ms and maintains a safe stopping distance of 8.5 m for pedestrians, while also shortening stop duration and overall traversal time. These results indicate that the proposed system provides robust and scalable performance at smart intersections.

eess.SY↗
arXiv2026

An isoperimetric inequality for Neumann eigenvalues with radial log-concave measures

We prove a sharp isoperimetric inequality for the harmonic mean of the first $n$ nonzero Neumann eigenvalues of the Witten-Laplacian on origin-symmetric Lipschitz domains in space forms, endowed with radial log-concave measures. The main novelty is that we establish the sharp harmonic mean inequality under general radial log-concave measures, without assuming the weight function to be non-increasing. This extends previous results that were restricted to specific or more restrictive weighted settings. The proof relies on a refined analysis of the first eigenfunction on geodesic balls, a monotonicity property derived from a convexity condition on the radial weight, and a matrix trace inequality.

math.SP↗
arXiv2026

Faber Krahn inequality of Robin eigenvalue of the Weighted Laplacian

In this paper, we study the isoperimetric inequalities for the Robin eigenvalues of the weighted Laplacian with positive Robin parameter in the Euclidean space $\R^n$ and the hyperbolic space $\mathbb{H}^n$, respectively. More precisely, we prove that among all bounded Lipschitz domains with fixed weighted volume, the geodesic ball centered at the origin minimizes the first Robin eigenvalue of the weighted Laplacian, provided that the Robin parameter and the radial log-convex density satisfy suitable conditions. Furthermore, we show that the second Robin eigenvalue is bounded below by the first Robin eigenvalue of the geodesic ball centered at the origin with half the weighted volume. Our results extend classical Faber-Krahn inequalities to the setting of weighted spaces with log-convex densities. We also derive a lower bound for the second Robin eigenvalue in terms of the first eigenvalue of the centered ball with half the weighted volume.

math.SP↗
arXiv2026

To $1/2$-logconcavity and beyond: Geometric properties of Dirichlet eigenfunctions

We prove that, on a bounded open convex domain $Ω\subset\mathbb{R}^n$, the first Dirichlet eigenfunction of the Laplacian or the Ornstein--Uhlenbeck operator is $α$-logconcave for every $α\in(0,1/2]$. This extends the recent $1/2$-logconcavity theorem of Crasta--Fragalà for the Laplacian to the weighted Gaussian setting and, simultaneously, to a broader range of exponents. More precisely, if $u$ denotes the first eigenfunction normalized by $\|u\|_\infty=1$, then for every $α\in(0,1/2]$, the function $-\bigl(-\log(κu(x))\bigr)^α$ is concave in $Ω$ provided the scaling parameter $κ$ lies below an explicit threshold $κ_α(Ω)\in(0,1)$, which depends on the first Dirichlet eigenvalue and on the diameter of~$Ω$. For the Ornstein--Uhlenbeck operator, $κ_α(Ω)$ also depends on the distance between $Ω$ and the origin. Moreover, we establish a local counterpart: for every $κ\in(0,1)$, the function $\bigl(-\log(κu)\bigr)^α$ is convex on a convex neighborhood $Ω_κ$ of the unique maximum point of~$u$. We also provide counterexamples showing that unscaled $1/2$-logconcavity may fail for the first Dirichlet eigenfunction of a Schrödinger operator with a smooth convex potential, and for the first Dirichlet eigenfunction of a weighted Laplacian associated with an affine log-concave weight.

math.AP↗
arXiv2026

Transformer Architecture with Minimal Inference Latency for Multi-Modal Wireless Networks

Next-generation wireless networks are expected to leverage multi-modal data sources to execute various wireless communication tasks such as beamforming and blockage prediction with situational-awareness. To do so, multi-modal transformers emerged as an effective tool, however, existing transformer-based approaches suffer from high inference latency and large memory footprints when processing multi-modal data. Hence, such existing solutions cannot handle wireless communication tasks that require fast inference to track a dynamically changing environment with moving vehicles and blockages. One major bottleneck is the reliance on attention mechanisms whose complexity grows quadratically with respect to the number of tokens. Hence, in this paper, a novel, fast multi-modal transformer inference framework is designed to practically support wireless communication tasks by processing only important tokens. To this end, an optimization problem is formulated to find the optimal number of tokens under a target FLOPs for a given wireless communication task while maintaining the task accuracy. To solve this problem, modality-specific tokenizers are first designed to project each modality into the same embedding dimension. Then, a token router is introduced to learn the importance of each token and process only important tokens. Subsequently, a trainable keep ratio is introduced to learn how many tokens to process for each layer under the target FLOPs. Simulation results show that, on DeepSense 6G beamforming tasks, we can reduce the inference latency, GPU memory, and FLOPs by 86.2% 35%, and 80%, respectively, with negligible accuracy loss. To validate the feasibility for real-world deployments, a multi-modal handover dataset is developed using a real-world testbed. Emulation results on the developed dataset show that the proposed framework can proactively initiate handover before blockage.

eess.SY↗
arXiv2026

An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian

In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our main theorem states that the ball centered at the origin maximizes the second Robin eigenvalue among all Lipschitz bounded domains of prescribed weighted measure and symmetric about the origin for a range of negative Robin parameters.

math.AP↗
arXiv2026

Cone Conditions for the Curvature Operator of the Second Kind on Einstein Manifolds

In this note, we study Einstein manifolds whose curvature operator of the second kind $\mathring{R}$ satisfies the cone condition \[ α^{-1}\big(\sum_{i=1}^{[α]} λ_i+ (α- [α] ) λ_{[α] + 1} \big) \ge -θ\barλ \] for some real number $α\in [1, (n+2)(n-1)/2)$. Here $[α] :=\max\{ m \in \mathbb{Z}: m \leq α\}$, $θ>-1$ and $λ_1 \le \cdots \le λ_{(n+2)(n-1)/2}$ are the eigenvalues of $\mathring{R}$ and $\barλ$ is their average. The main result states that any closed Einstein manifold of dimension $n \ge 4$ with $\mathring{R}$ satisfies the cone condition is flat or a round sphere. These results generalize recent works corresponding to $α\in \mathbb Z_+$ of the authors \cite{CW24-1,CW25-2} and Fu-Lu \cite{FL25}.

math.DG↗
arXiv2025

Einstein manifolds of negative lower bounds on curvature operator of the second Kind

We demonstrate that $n$-dimension closed Einstein manifolds, whose smallest eigenvalue of the curvature operator of the second kind of $\mathring{R}$ satisfies $λ_1 \ge -θ(n) \barλ$, are either flat or round spheres, where $\bar λ$ is the average of the eigenvalues of $\mathring{R}$, and $θ(n)$ is defined as in equation (1.2). Our result improves a celebrated result (Theorem 1.1) concerning Einstein manifolds with nonnegative curvature operator of the second kind.

math.DG↗
arXiv2025

Parabolic Frequency on Gaussian Spaces and Unique Continuation

We establish an almost-monotonicity formula for a parabolic frequency on Gaussian spaces for solutions of the Ornstein-Uhlenbeck heat equation with lower-order terms: $$\partial_t u = L_γu + b(x,t) \cdot \nabla u + c(x,t)u, $$ where $L_γ= Δ- x \cdot \nabla$ is the Ornstein-Uhlenbeck operator. In contrast to classical results that require $b$ and $c$ to be bounded, we only assume that $b$ is bounded and $c$ satisfies a linear growth condition, while the solution $u$ is allowed to have at most exponential quadratic growth. The key innovation is a weighted $L^2$ framework that uses the backward Mehler kernel as a weight, which naturally encodes the underlying measure and compensates for the unbounded coefficients. From the frequency monotonicity, we derive the strong unique continuation principle. This extends Poon's seminal results and complements recent geometric generalizations by Colding and Minicozzi in the context of Gaussian measure spaces. We further apply our framework to establish unique continuation for equations with potentials exhibiting quadratic growth or certain singularities.

math.AP↗
arXiv2025

Sharp Fundamental Gap Estimate on Convex Domains in Gaussian Spaces

We prove a sharp lower bound for the fundamental gap on convex domains in Gaussian spaces, the difference between the first two eigenvalues of the Ornstein-Uhlenbeck operator with Dirichlet boundary conditions. Our main result establishes that the gap is bounded below by the gap of the corresponding one-dimensional model, confirming the Gaussian analogue of the fundamental gap conjecture. Furthermore, we demonstrate that the normalized gap of the one-dimensional model is monotonically increasing with the diameter and prove the sharpness of our estimate. Beyond the fundamental gap, we also establish improved log-concavity properties for the Dirichlet heat kernel on convex domains in Gaussian spaces. Our work on Gaussian spaces complements the existing results of Andrews and Clutterbuck and Ni for Euclidean domains, as well as the work of Seto, Wang, and Wei for spherical domains.

math.SP↗
arXiv2025

Digital Twin-based Cooperative Autonomous Driving in Smart Intersections: A Multi-Agent Reinforcement Learning Approach

Unsignalized intersections pose safety and efficiency challenges due to complex traffic flows and blind spots. In this paper, a digital twin (DT)-based cooperative driving system with roadside unit (RSU)-centric architecture is proposed for enhancing safety and efficiency at unsignalized intersections. The system leverages comprehensive bird-eye-view (BEV) perception to eliminate blind spots and employs a hybrid reinforcement learning (RL) framework combining offline pre-training with online fine-tuning. Specifically, driving policies are initially trained using conservative Q-learning (CQL) with behavior cloning (BC) on real datasets, then fine-tuned using multi-agent proximal policy optimization (MAPPO) with self-attention mechanisms to handle dynamic multi-agent coordination. The RSU implements real-time commands via vehicle-to-infrastructure (V2I) communications. Experimental results show that the proposed method yields failure rates below 0.03\% coordinating up to three connected autonomous vehicles (CAVs), significantly outperforming traditional methods. In addition, the system exhibits sub-linear computational scaling with inference times under 40 ms. Furthermore, it demonstrates robust generalization across diverse unsignalized intersection scenarios, indicating its practicality and readiness for real-world deployment.

eess.SY↗
arXiv2025

Einstein manifolds under cone conditions for the curvature operator of the second kind

It is established in [6, 14, 23] that any closed Einstein manifold with two-nonnegative curvature operator of the second kind is either flat or a round sphere. In this paper, we refine this result by relaxing the curvature condition to a cone condition (strictly weaker than two nonnegativity) proposed by Li [18]. Precisely, we prove that any closed Einstein manifold of dimension $n=4$ or $n=5$ or $n\ge 8$, if the curvature operator of the second kind $\mathring{R}$ satisfies \begin{align*} (λ_1+λ_2)/2 \ge -θ(n) \bar λ, \end{align*} then the manifold is either flat or a round sphere. Here, $λ_1\le λ_2\le \cdots\le λ_{(n-1)(n+2)/2}$ are the eigenvalues of $\mathring{R}$, $ \bar λ$ is their average, and $θ(n)$ is a positive constant defined as in (1.2).

math.DG↗
arXiv2025

X-ray Diffraction and Electrical Transport Imaging of Superconducting Superhydride (La,Y)H10

We report the synthesis and characterization of (La0.9Y0.1)H10 superhydrides exhibiting coexisting cubic Fm-3m and hexagonal P63/mmc clathrate phases observed over the pressure range from 168 GPa down to 136 GPa. Using synchrotron-based X-ray diffraction imaging (XDI) at the upgraded Advanced Photon Source (APS-U), we spatially resolved micron-scale distributions of these phases, revealing structural inhomogeneity across the sample. Four-probe DC resistance measurements confirmed superconductivity, with two distinct transitions: an onset at 244 K associated with the cubic phase and a second near 220 K linked to the hexagonal phase. Notably, resistance profiles collected from different current and voltage permutations showed variations in transition width and onset temperature that correlated with the spatial phase distribution mapped by XDI. These findings demonstrate a direct connection between local structural domains and superconducting behavior. Yttrium substitution is found to influence both the phase behavior and superconducting properties of LaH10-type clathrate hydrides. More broadly, this study highlights the utility of spatially correlating structural and electrical transport measurements in materials exhibiting heterogeneity under pressure, including hydride superconductors.

cond-mat.supr-con↗
arXiv2025

The Robin heat kernel and its expansion via Robin eigenfunctions

We prove the existence and uniqueness of the Robin heat kernel on compact Riemannian manifolds with smooth boundary for Robin parameter $α\in\mathbb{R}$, expressed as a spectral expansion in terms of Robin eigenvalues and eigenfunctions. For the non-negative parameter regime ($α\ge 0$), we present a direct proof based on trace Sobolev inequalities and eigenfunction estimates. The case of negative parameters ($α<0$) requires novel analytical techniques to handle $L^\infty$ estimates of Robin eigenfunctions, addressing challenges not present in the non-negative case. Our result extends the the classical Dirichlet and Neumann cases to the less-studied negative parameter regime.

math.AP↗
arXiv2025

Multi-Agent Reinforcement Learning-based Cooperative Autonomous Driving in Smart Intersections

Unsignalized intersections pose significant safety and efficiency challenges due to complex traffic flows. This paper proposes a novel roadside unit (RSU)-centric cooperative driving system leveraging global perception and vehicle-to-infrastructure (V2I) communication. The core of the system is an RSU-based decision-making module using a two-stage hybrid reinforcement learning (RL) framework. At first, policies are pre-trained offline using conservative Q-learning (CQL) combined with behavior cloning (BC) on collected dataset. Subsequently, these policies are fine-tuned in the simulation using multi-agent proximal policy optimization (MAPPO), aligned with a self-attention mechanism to effectively solve inter-agent dependencies. RSUs perform real-time inference based on the trained models to realize vehicle control via V2I communications. Extensive experiments in CARLA environment demonstrate high effectiveness of the proposed system, by: \textit{(i)} achieving failure rates below 0.03\% in coordinating three connected and autonomous vehicles (CAVs) through complex intersection scenarios, significantly outperforming the traditional Autoware control method, and \textit{(ii)} exhibiting strong robustness across varying numbers of controlled agents and shows promising generalization capabilities on other maps.

cs.RO↗