An integral formula with geometric applications in Riemannian and Pseudo-Riemannian manifolds

12/09/2015 - 13:30
12/09/2015 - 14:30
Junfang Li (University of Alabama)
Burnside Hall Room 920 (McGill University)

In this talk, we will present a recent joint work with Chao 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) Heitz-Karcher type inequalities, 2) Minkowski inequality, 3) two almost Schur type of Theorems. All these geometric inequalities hold for the so-called 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 Pseudo-Riemannian spaces.

Last edited by on Wed, 12/02/2015 - 14:47