February 5, Junfang Li, UABMath Colloquium: Fri at 2:30pm-3:20pm, CH 443
Title. An integral formula on Riemannian and Semi-Riemannian manifolds
Abstract. In this talk, we will present a recent joint work with C. Xia. We first prove a general integral formula for bounded domains in Riemannian manifolds. This formula includes Reilly's integral formula and the recent work of Qiu-Xia as special cases. In the second part of the talk, we will apply this formula to prove 1) Heitnz-Karcher type inequalities, 2) Minkowski inequality, 3) two almost Schur type of Theorems. All these geometric inequalities hold for the substatic Riemannian manifolds which consists of a large family Riemannian manifolds including all the space forms. We note that Heitze-Karcher inequality naturally leads to an Alexandrov rigity theorem for substatic warped product spaces. Thus we recovered S. Brendle's recent work by a completely different approach. The results in this talk are focused on Riemannian manifolds, however it has deep roots from Semi-Riemannian spacetimes.
- On June 30 Kyle Besing successfully defended his Ph.D. thesis Spectral properties and localization of two random Laplacians on graphs. His studies were directed by Dr. G. Stolz.
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