Hyper-elastic Ricci flow: Gradient flow, local existence-uniqueness, and a Perelman energy functional

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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description 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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title Hyper-elastic Ricci flow: Gradient flow, local existence-uniqueness, and a Perelman energy functional
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