This is the geometric analysis seminar at SCMS. Everyone is welcome.
Organizers: Zhichao Wang
Speaker: Liangming Shen
Date and time: Oct 22, 10:00--11:00
Venue: SCMS 106
Abstract: Using smooth approximation method of conic Kahler metrics, we could establish existence and extend Li-Yau's classical estimates of the heat kernel for conic Kahler metrics. Then we can give some eigenvaluve estimates for such metrics.
Speaker: Xiaoshang Jin
Date and time: Oct 22, 11:00--12:00
Venue: SCMS 106
Abstract: In this talk, we will discuss Dirichlet eigenvalue asymptotics on conformally compact Einstein manifolds. We begin with the geometry of conformal infinity and its relation to the Einstein interior, followed by classical spectral results. For large geodesic balls, we describe a two-term expansion at the threshold, governed by the continued resolvent and threshold resonance. We also present a sharp large-ball expansion for the nonlinear p-Laplacian under nonnegative Yamabe infinity, identifying its exact second coefficient and briefly outlining the main ideas.
Speaker: Jianchun Chu
Date and time: Oct 15, 10:00--11:00
Venue: SCMS 106
Abstract: The mixed curvature comes from a linear combination of the Ricci and holomorphic sectional curvature. In this talk, we will first survey recent progress. Then we discuss a structure theorem for compact Kahler manifolds with non-negative mixed curvature. This is a joint work with Man-Chun Lee and Jintian Zhu.