no. 21-22
Differential geometry
A note on Chowʼs entropy functional for the Gauss curvature flow
[Note sur la fonctionnelle dʼentropie de Chow relative au flot de la courbure de Gauss]

Présenté par : the Editorial Board

Guo, Hongxin1 ; Philipowski, Robert2 ; Thalmaier, Anton2
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, Tome 351 (2013) no. 21-22, pp. 833-835.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.003
Guo, Hongxin 1 ; Philipowski, Robert 2 ; Thalmaier, Anton 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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Guo, Hongxin; Philipowski, Robert; Thalmaier, Anton. A note on Chowʼs entropy functional for the Gauss curvature flow. Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 833-835. doi : 10.1016/j.crma.2013.10.003. http://www.numdam.org/articles/10.1016/j.crma.2013.10.003/

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

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

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

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

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

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