Perelman's $W$-functional on manifolds with conical singularities

Abstract

In this paper, we develop the theory of Perelman's $W$-functional on manifolds with isolated conical singularities. In particular, we show that the infimum of $W$-functional over a certain weighted Sobolev space on manifolds with isolated conical singularities is finite, and the minimizer exists, if the scalar curvature satisfies certain condition near the singularities. We also obtain an asymptotic order for the minimizer near the singularities.

References in corpus (1)

• Gaussian densities and stability for some Ricci solitons

Cited by in corpus (4)

• A Survey on the Ricci flow on Singular Spaces
• Perelman's Entropies for Manifolds with conical Singularities
• Functional Inequalities on Simple Edge Spaces
• Stability of the conical Kähler-Ricci flows on Fano manifolds