Differential Geometry
An entropy formula relating Hamiltonʼs surface entropy and Perelmanʼs W entropy
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 115-118.

In this note, based on Hamiltonʼs surface entropy formula, we construct an entropy formula of Perelmanʼs type for the Ricci flow on a closed surface with positive curvature. Similar to Perelmanʼs W entropy, the critical point of our entropy is the gradient shrinking soliton; however, there is no conjugate heat equation involved. This shows a close relation between Hamiltonʼs entropy and Perelmanʼs W entropy on closed surfaces.

Dans cette note, à partir de la formule de Hamilton pour lʼentropie des surfaces, nous construisons une formule dʼentropie de type Perelman pour le flot de Ricci sur une surface fermée à courbure positive. De même que pour lʼentropie W de Perelman, le point critique de notre entropie est le soliton gradient décroissant, bien quʼil nʼy ait pas ici dʼéquation de la chaleur qui soit mise en jeu. Ceci démontre une relation étroite entre lʼentropie de Hamilton et lʼentropie W de Perelman sur les surfaces fermées.

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Accepted:
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DOI: 10.1016/j.crma.2013.03.003
Guo, Hongxin 1

1 School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
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Guo, Hongxin. An entropy formula relating Hamiltonʼs surface entropy and Perelmanʼs $ \mathcal{W}$ entropy. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 115-118. doi : 10.1016/j.crma.2013.03.003. http://www.numdam.org/articles/10.1016/j.crma.2013.03.003/

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