Hyper-elastic Ricci flow: Gradient flow, local existence-uniqueness, and a Perelman energy functional
The equation of hyper-elastic Ricci flow amends classical Ricci flow by the addition of the Cauchy stress tensor which itself is derived from the a free energy. In this paper hyper-elastic Ricci flow is shown to possess three properties derived by G. Perelman for classical Ricci flow, specifically i...
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Veröffentlicht in: | Quarterly of applied mathematics 2023-12, Vol.81 (4), p.599-613 |
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Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | The equation of hyper-elastic Ricci flow amends classical Ricci flow by the addition of the Cauchy stress tensor which itself is derived from the a free energy. In this paper hyper-elastic Ricci flow is shown to possess three properties derived by G. Perelman for classical Ricci flow, specifically it is diffeomorphically equivalent to a gradient flow, unique smooth solutions exist locally in time, and the system possesses a non-decreasing energy function. |
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ISSN: | 0033-569X 1552-4485 |
DOI: | 10.1090/qam/1643 |