**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.