arXiv subjects

Inbo Gottlieb Fenves

Publications and source records attributed to Inbo Gottlieb Fenves.

3 recordsLinked to original sources

arXiv2026

Sharp lower bounds for the periodic maximal Schrödinger operator in higher dimensions

We prove sharp lower bounds for the Schrödinger maximal function on the torus T^d for all dimensions d at least 2, and as a corollary obtain sharp regularity conditions for pointwise convergence of the periodic Schrödinger equation. Combined with sufficiency results established by Compaan-Lucá-Staffilani, this yields a full resolution of Carleson's problem up to endpoint for the periodic Schrödinger equation in all dimensions at least 2, and disproves the conjectured regularity condition of Miao-Yuan-Zhao, in contrast to the corresponding question in R^d. We also prove sharp estimates on the dimensions of divergence sets for the equation for high dimensional tori. Our approach uses complex multiplication on abelian varieties.

math.CA↗

arXiv2026

Maximal estimates for perturbations of the Schrödinger operator on $\mathbb{T}^d$

We study $L^p_x L^\infty_t$ maximal estimates for exponential sums associated to $C^2$ graph hypersurfaces, motivated by Schrödinger maximal estimates on $\mathbb{T}^d$. We show that the conjectured maximal estimate for the periodic Schrödinger equation fails when one allows small perturbations of the paraboloid, which can be viewed as a higher-dimensional extension of the phenomenon proved by Fu, Ren, and Wang. Our approach uses new lower bounds for incidence estimates originally proven by Cairo and Zhang, for which we provide an alternative proof based on homogeneous dynamics. Moreover the estimates are essentially sharp at the decoupling endpoint for the paraboloid $p = \frac{2(d+2)}{d}$.

math.CA↗

arXiv2026

Cusp Excursions, Lattice Points on Manifolds, and the Mizohata-Takeuchi Conjecture

We prove new logarithm laws for cusp excursions in spaces of lattices, and produce quantitative lower bounds for lattice points near submanifolds, using tools from dynamics and the geometry of numbers. As an application, we provide a new proof of power loss for the local Mizohata-Takeuchi conjecture with explicit error terms, as well as show that power loss is generic in $C^k$. The construction uses high-dimensional probabilistic estimates, but replaces the random orthogonal subspaces of Cairo-Zhang with random unimodular lattices; this yields stronger bounds and provides a richer family of counterexamples.

math.DS↗