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.
On the maximal mean curvature of a smooth surface / Ferone, Vincenzo; Nitsch, Carlo; Trombetti, Cristina. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 354:9(2016), pp. 891-895. [10.1016/j.crma.2016.05.018]
On the maximal mean curvature of a smooth surface
FERONE, VINCENZO;NITSCH, CARLO;TROMBETTI, CRISTINA
2016
Abstract
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.File in questo prodotto:
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