Perelman’s entropies for manifolds with conical singularities

Kröncke, Klaus; Vertman, Boris

doi:10.1090/tran/8295

Perelman’s entropies for manifolds with conical singularities

Authors: Klaus Kröncke and Boris Vertman
Journal: Trans. Amer. Math. Soc. 374 (2021), 2873-2908
MSC (2020): Primary 53E20; Secondary 53C25, 58C05
DOI: https://doi.org/10.1090/tran/8295
Published electronically: January 21, 2021
MathSciNet review: 4223036
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Abstract: In this paper we discuss Perelman’s $\lambda$-functional, Perelman’s Ricci shrinker entropy as well as the Ricci expander entropy on a class of manifolds with isolated conical singularities. On such manifolds, a singular Ricci de Turck flow preserving the isolated conical singularities exists by our previous work. We prove that the entropies are monotone along the singular Ricci de Turck flow. We employ these entropies to show that in the singular setting, Ricci solitons are gradient and that steady or expanding Ricci solitons are Einstein.

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