# Geometry Seminar

## \epsilon-Regularity for 4-dimensional shrinking Ricci solitons

Shaosai Huang, Stony Brook University

Monday, October 2nd, 2017
2:00 PM - 3:00 PM
Hylan 1106A

A central issue in studying uniform behaviors of Riemannian manifolds is to obtain uniform local L^{\infty}-bounds of the curvature tensor. For manifolds whose Riemannian metric satisfying certain elliptic equations, e.g. Einstein manifolds and Ricci solitons, local curvature bound could be obtained when the local energy is sufficiently small. Such estimates, referred to as \epsilon-regularity, are usually obtained via Moser iteration arguments, which requires a uniform control of the Sobolev constant. This requirement may fail in many natural situations. In this talk, I will discuss an \epsilon-regularity result for 4-dimensional shrinking Ricci solitons without a priori control of the Sobolev constant.

Event contact: yzeng15 at ur dot rochester dot edu