Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
王凤雨 教授，天津大学
Inviter:
何凯 博士
Title:
Identifying Einstein Manifolds Using Stochastic Analysis
Time & Venue:
2018.12.4 8:30 N204
Abstract:
We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. Combining these with derivative and Hessian formulas of the heat semigroup developed from stochastic analysis, we identify constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds by using analytic formulas and semigroup inequalities. Moreover, explicit Hessian estimates are derived for the heat semigroup on Einstein and Ricci parallel manifolds.