Differential Geometry Seminar: $\epsilon$-Regularity for 4-dimensional shrinking Ricci solitons

Seminar | November 20 | 1-2 p.m. | 891 Evans Hall

Shaosai Huang, Stony Brook

Department of Mathematics

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 are expected 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 $\textit {without}$ a priori control of the Sobolev constant.

rbamler@berkeley.edu