Comptes Rendus
no. 21-22
Differential geometry
A note on Chowʼs entropy functional for the Gauss curvature flow

Presented by: the Editorial Board

Hongxin Guo1; Robert Philipowski2; Anton Thalmaier2
1 School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
2 Unité de Recherche en Mathématiques, FSTC, Université du Luxembourg, 6, rue Richard-Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg
Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 833-835.

Based on the entropy formula for the Gauss curvature flow introduced by Bennett Chow, we define an entropy functional that is monotone along the unnormalized flow and whose critical point is a shrinking self-similar solution.

À partir de la formule dʼentropie introduite par Bennett Chow pour le flot de la courbure de Gauss, nous définissons une entropie qui est monotone le long du flot non normalisé, et dont le point critique est une solution auto-similaire contractante.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.003

Hongxin Guo 1; Robert Philipowski 2; Anton Thalmaier 2

1 School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
2 Unité de Recherche en Mathématiques, FSTC, Université du Luxembourg, 6, rue Richard-Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg 
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Hongxin Guo; Robert Philipowski; Anton Thalmaier. A note on Chowʼs entropy functional for the Gauss curvature flow. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 833-835. doi : 10.1016/j.crma.2013.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.003/

[1] Bennett Chow On Harnackʼs inequality and entropy for the Gaussian curvature flow, Commun. Pure Appl. Math., Volume 4 (1991) no. 4, pp. 469-483

[2] Pengfei Guan; Lei Ni Entropy and a convergence theorem for Gauss curvature flow in high dimension | arXiv

[3] Hongxin Guo An entropy formula relating Hamiltonʼs surface entropy and Perelmanʼs W entropy, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013) no. 3–4, pp. 115-118

[4] Richard S. Hamilton The Ricci flow on surfaces, Santa Cruz, CA, 1986 (Contemp. Math.), Volume vol. 71 (1988), pp. 237-262

[5] Richard S. Hamilton Remarks on the entropy and Harnack estimates for the Gauss curvature flow, Commun. Anal. Geom., Volume 2 (1994) no. 1, pp. 155-165

[6] Grisha Perelman The entropy formula for the Ricci flow and its geometric applications | arXiv

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