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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.01863 |
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| _version_ | 1866918272271646720 |
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| author | Chow, Tsz-Kiu Aaron Fong, Frederick Tsz-Ho |
| author_facet | Chow, Tsz-Kiu Aaron Fong, Frederick Tsz-Ho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Spinorial Perelman's Functional: Critical Points and Gradient Flow Chow, Tsz-Kiu Aaron Fong, Frederick Tsz-Ho Differential Geometry 53E20, 53C27 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. |
| title | A Spinorial Perelman's Functional: Critical Points and Gradient Flow |
| topic | Differential Geometry 53E20, 53C27 |
| url | https://arxiv.org/abs/2601.01863 |