Speaker: Jing MAO （Hubei University）

Time： Dec 07, 16:00-17:00

Place： 腾讯会议：249-108-389 会议密码：202222

Title： Polya-type inequalities on spheres and hemispheres

Abstract： Given an eigenvalue $\lambda$ of the Laplace-Beltrami operator on n-spheres and -hemispheres, we characterise those with the lowest and highest orders which equal $\lambda$ and for which Polya's conjecture holds and fails. We further derive Polya-type inequalities by adding a correction term providing sharp lower and upper bounds for all eigenvalues. This allows us to measure the deviation from the leading term in the Weyl asymptotics for eigenvalues on spheres and hemispheres. As a direct consequence, we obtain similar results for domains which tile hemispheres. This talk is based on a joint-work with Prof. Pedro Freitas AND Prof. Isabel Salavessa.