Comptes Rendus
no. 9
Mathematical analysis
On the maximal mean curvature of a smooth surface

Presented by: Haïm Brézis

Vincenzo Ferone1; Carlo Nitsch1; Cristina Trombetti1
1 Università degli Studi di Napoli Federico II, Napoli, Italy
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 891-895.

Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the maximal curvature alone. We show that in higher dimensions this is not true, and for a given maximal mean curvature we provide smooth embeddings of the ball with arbitrary small volume.

Étant donné un domaine planaire simplement connexe lisse, l'aire est bornée loin de zéro en termes de la seule courbure maximale. Nous montrons que pour des dimensions plus élevées ce n'est pas vrai, et nous fournissons, pour un maximum donné de la courbure moyenne, des plongements lisses de la boule avec un petit volume arbitraire.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.05.018

Vincenzo Ferone 1; Carlo Nitsch 1; Cristina Trombetti 1

1 Università degli Studi di Napoli Federico II, Napoli, Italy 
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Vincenzo Ferone; Carlo Nitsch; Cristina Trombetti. On the maximal mean curvature of a smooth surface. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 891-895. doi : 10.1016/j.crma.2016.05.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.05.018/

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