报告题目：Weighted versions of scalar curvature, mass and spin geometry for Ricci flows

报告人：Tristan Ozuch (MIT)

时间：2022年4月21日 09:00-10:00

地点：腾讯会议号：914-3694-1759，密码：202202

摘要：With A. Deruelle, we define a Perelman like functional for ALE metrics which lets us study the (in)stability of Ricci-flat ALE metrics. With J. Baldauf, we extend some classical objects and formulas from the study of scalar curvature, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.