[Sur la courbure moyenne maximale d'une surface lisse]
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.
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.
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@article{CRMATH_2016__354_9_891_0,
author = {Ferone, Vincenzo and Nitsch, Carlo and Trombetti, Cristina},
title = {On the maximal mean curvature of a smooth surface},
journal = {Comptes Rendus. Math\'ematique},
pages = {891--895},
publisher = {Elsevier},
volume = {354},
number = {9},
year = {2016},
doi = {10.1016/j.crma.2016.05.018},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.05.018/}
}
TY - JOUR AU - Ferone, Vincenzo AU - Nitsch, Carlo AU - Trombetti, Cristina TI - On the maximal mean curvature of a smooth surface JO - Comptes Rendus. Mathématique PY - 2016 SP - 891 EP - 895 VL - 354 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.05.018/ DO - 10.1016/j.crma.2016.05.018 LA - en ID - CRMATH_2016__354_9_891_0 ER -
%0 Journal Article %A Ferone, Vincenzo %A Nitsch, Carlo %A Trombetti, Cristina %T On the maximal mean curvature of a smooth surface %J Comptes Rendus. Mathématique %D 2016 %P 891-895 %V 354 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.05.018/ %R 10.1016/j.crma.2016.05.018 %G en %F CRMATH_2016__354_9_891_0
Ferone, Vincenzo; Nitsch, Carlo; Trombetti, Cristina. On the maximal mean curvature of a smooth surface. Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 891-895. doi : 10.1016/j.crma.2016.05.018. http://www.numdam.org/articles/10.1016/j.crma.2016.05.018/
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