Heat kernel expansions, Tauberian theory and Weyl law for Schrodinger operator on noncompact manifolds

：颜俊榕（美国东北大学）
：2025-07-17 10:00
：海韵园实验楼S105

报 告 人：颜俊榕（美国东北大学）

时  间：2025年7月17日10:00

地  点：海韵园实验楼S105

内容摘要:

The classical Weyl law for Schrödinger operators on noncompact manifolds has long been anticipated, yet remains unestablished in full generality. Existing results are largely confined to Euclidean spaces or to manifolds with specific geometric or topological structures at infinity. Standard techniques such as the Dirichlet bracketing method, though effective in \mathbb{R}^n, encounter intrinsic difficulties in more general noncompact settings. In this talk, I will present an extended Tauberian framework, combined with new heat kernel asymptotics tailored to noncompact manifolds, which enables us to derive the Weyl law under broad assumptions. Remarkably, our method requires only mild regularity on the potential—even weaker than what is typically assumed in the Euclidean case.

个人简介：

颜俊榕，博士，毕业于加州大学圣芭芭拉分校，师从戴先哲教授。目前在美国东北大学（波士顿）从事博士后研究工作。主要研究方向为谱理论、整体微分几何以及数学物理中的相关问题。相关工作发表在JIMJ, Math. Z.和JGP上。

 

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