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Haiping Fu

Publications and source records attributed to Haiping Fu.

8 recordsLinked to original sources
arXiv2026

Monotone quantities on $3$-manifolds with nonnegative scalar curvature

In this paper, we derive monotone quantities for harmonic functions on asymptotically flat 3-manifolds with simple topology and nonnegative scalar curvature. These monotone quantities are constant on spatial Schwarzschild manifolds outside rotationally symmetric spheres. To derive monotone quantities, our method is different from the ODE analysis in Xia-Yin-Zhou \cite{Xia} and Mazurowski-Yao \cite{Maz}, we follow the strategy developed in Miao \cite{Miao}. As applications, we recover and generalize some geometric inequalities and mass-capacity inequalities in Miao \cite{Miao} and Oronzio \cite{Oronzio}. Furthermore, we obtain the integral identities for the mass-capacity ratio which is parallel to the results in Miao \cite{Miao}.

math.DG↗
arXiv2026

Physics-Informed Neural Networks for Radial Consolidation of Combined Electroosmotic, Vacuum and Surcharge Preloading Considering Smear Effects

This study develops a dimensionless multi-domain physics-informed neural network (PINN) framework for electro-osmotic radial consolidation considering smear effects and combined vacuum and surcharge loading. Three PINN-based models are investigated: a standard soft-constrained PINN (Std-PINN), a modified gated PINN (Mod-PINN), and a modified gated PINN with hard-constraint boundary encoding (Mod-HC-PINN). The models are evaluated against FEM reference solutions under four loading cases, including constant vacuum, exponential vacuum, exponential vacuum with ramp surcharge, and exponential vacuum with cyclic haversine surcharge. The results indicate that the gated architecture applied in Mod-PINN improves the resolution of steep pressure gradients near the cathode and smear-zone interface under constant vacuum loading. Under time-dependent loading, the soft-constrained Mod-PINN shows reduced accuracy because it must learn multiple competing objectives simultaneously. The Mod-HC-PINN mitigates this issue by embedding the cathode boundary and initial conditions into the output structure, thereby reducing the optimization burden and improving physical consistency. The Mod-HC-PINN achieves MAE values of 0.43, 0.41, and 0.27 kPa for the exponential vacuum, ramp surcharge, and cyclic surcharge cases, respectively. Sensitivity analyses further demonstrate that the proposed framework remains robust across practical ranges of network architecture, collocation density, and permeability contrast.

cs.CE↗
arXiv2026

Manifolds with harmonic Weyl curvature and curvature operator of the second kind

We prove that a compact Riemannian manifold of dimension $n\ge 8$ with harmonic Weyl curvature and $\frac{3(n-1)(n+2)}{4(3n-1)}$-nonnegative curvature operator of the second kind is either globally conformally equivalent to a space of positive constant curvature or is isometric to a flat manifold. In particular, We also give a classification of four-dimensional manifolds with harmonic Weyl curvature satisfying a cone condition. This result generalizes the work in \cite{DFY24,FLD,Li22}.

math.DG↗
arXiv2026

Manifolds with harmonic curvature and curvature operator of the second kind

We prove that complete Riemannian manifolds of dimension $n\ge3$ with harmonic curvature and $\frac{n(n+2)}{2(n+1)}$-nonnegative curvature operator of the second kind must be Einstein. In particular, We show that complete Einstein manifolds of dimension $n\ge4$ with $\frac{3n(n-1)^2(n+2)}{2(5n^3+3n^2-30n+16)}$-nonnegative curvature operator of the second kind must be of constant curvature, which generalizes the work of Dai-Fu \cite{DF}.

math.DG↗
arXiv2025

New rigidity theorem of Einstein manifolds and curvature operator of the second kind

Using Bochner techniques, we prove that a compact Einstein manifold of dimension $n \ge 4$ has constant curvature provided that the curvature operator of the second kind satisfies a cone condition that is strictly weaker than nonnegativity. Furthermore, employing a result of Li \cite{Li5}, we establish that any closed Einstein manifold of dimension $n \ge 4$ satisfying \[k^{-1}({\lambda }_1+\cdots +{\lambda }_k)\ge -\theta(n,k) \bar{\lambda },\quad \text{for some} \quad k \le [\frac{n+2}{4}]\] must be either flat or a spherical space form. Here, ${\lambda }_1\le {\lambda }_2\le \cdots \le {\lambda }_{\frac{(n-1)(n+2)}{2}}$ are the eigenvalues of $\mathring{R}\,$, $\bar{\lambda }$ is their average, and $\theta (n,k)$ is a positive constant. This result generalizes the work of Dai-Fu \cite{DF} and Chen-Wang \cite{CW1,CW}.We also classify four-dimensional Einstein manifolds satisfying a cone condition.

math.DG↗
arXiv2018

On compact Riemannian manifolds with harmonic weyl curvature

We give some rigidity theorems for an n$(\geq4)$-dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $\sigma_2$. Moreover, when $n=4,$ we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant $\sigma_2$ is isometric to a quotient of the round $\mathbb{S}^4$.

math.DG↗