The Pólya conjecture and Li-Yau inequality for higher eigenvalues

Abstract: In this talk, we will talk about the Pólya conjecture and Li-Yau inequality for higher eigenvalues. We will first introduce the background and some results on higher eigenvalue problems for the Laplace operator on bounded domain in the Euclidean space. Then, we will discuss the generalizations for those results on compact minimal submanifolds with boundary. We will also discuss the estimates on the number of eigenvalues of the Schrödinger operator on compact minimal submanifolds with boundary. This is joint work with Prof. Hongwei Xu.

Mathematics

Audience: researchers in the topic

ICCM 2020