SMS scnews item created by Boris Lishak at Tue 28 Aug 2018 1419
Type: Seminar
Distribution: World
Calendar1: 29 Aug 2018 1200-1300
CalLoc1: Carslaw 830
CalTitle1: Kwok -- Some quantitative comparison theorems in Riemannian geometry
Auth: borisl@dora.maths.usyd.edu.au

Geometry and Topology Seminar

Some quantitative comparison theorems in Riemannian geometry

Kwok-Kun Kwong (Sydney)

Please join us for lunch at 1 p.m.

Abstract:

The classical volume comparison states that under a lower bound on the Ricci curvature, the volume of the geodesic ball is bounded from above by that of the ball with the same radius in the model space. On the other hand, counterexamples show that the assumption on the Ricci curvature cannot be weakened to a lower bound on the scalar curvature, which is the average of the Ricci curvature. In this talk, I will show that a lower bound on a weighted average of the Ricci curvature is sufficient to ensure volume comparison. In the course I will also show a sharp quantitative volume estimate, an integral version of the Laplacian comparison theorem, and some applications. If time allows, I will also present the Kahler version of the theorem.


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