Perelman’s entropies for manifolds with conical singularities
Copyright policy )Perelman’s entropies for manifolds with conical singularities
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.
41 pages
- Universität Hamburg Germany
- Carl von Ossietzky University of Oldenburg Germany
Mathematics - Differential Geometry, Real-valued functions on manifolds, Special Riemannian manifolds (Einstein, Sasakian, etc.), Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Ricci flows, Ricci flow, FOS: Mathematics, 53C44, 53C25, 58J05, singular spaces, Perelman's entropy, Ricci solitons, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, Real-valued functions on manifolds, Special Riemannian manifolds (Einstein, Sasakian, etc.), Mathematics - Analysis of PDEs, Differential Geometry (math.DG), Ricci flows, Ricci flow, FOS: Mathematics, 53C44, 53C25, 58J05, singular spaces, Perelman's entropy, Ricci solitons, Analysis of PDEs (math.AP)
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