A Spinorial Perelman's Functional: Critical Points and Gradient Flow
Differential Geometry
2026-01-06 v1
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.
Keywords
Cite
@article{arxiv.2601.01863,
title = {A Spinorial Perelman's Functional: Critical Points and Gradient Flow},
author = {Tsz-Kiu Aaron Chow and Frederick Tsz-Ho Fong},
journal= {arXiv preprint arXiv:2601.01863},
year = {2026}
}
Comments
23 pages. Comments are welcome!