Perelman's Functional for Manifolds with Conical Singularities

Xianzhe Dai (UC Santa Barbara)

Abstract

Perelman's entropy functional plays an important role in analyzing Ricci flow. We develop Perelman's entropy functional for manifolds with conical singularity. It involves a singular Schrodinger operator and the analysis of the asymptotic behavior of its eigenfunctions near the conical singularity. This is joint work with Changliang Wang.