A Spinorial Perelman's Functional: Critical Points and Gradient Flow

Tsz-Kiu Aaron Chow; Frederick Tsz-Ho Fong

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arXiv · 2601.01863

A Spinorial Perelman's Functional: Critical Points and Gradient Flow

Tsz-Kiu Aaron Chow·Frederick Tsz-Ho Fong

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Abstract

In this article, we introduce an energy functional on closed Riemannian spin manifolds which unifies Perelman's W- and F-functionals, Baldauf-Ouzch's E-functional, and Dirchlet energy for spinors. We compute its first variation formula, and show that its critical points under natural constraints are twisted Ricci solitons and eigen-spinsors of the weighted Dirac operator. We introduce a negative L^2-gradient flow of this functional, and establish its short-time existence and uniqueness via contraction mapping methods.

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Tsz-Kiu Aaron Chow, Frederick Tsz-Ho Fong. 2026-01-05. A Spinorial Perelman's Functional: Critical Points and Gradient Flow. https://arxiv.org/abs/2601.01863

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