On the maximal mean curvature of a smooth surface
Optimization and Control
2016-04-21 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1604.06042,
title = {On the maximal mean curvature of a smooth surface},
author = {Vincenzo Ferone and Carlo Nitsch and Cristina Trombetti},
journal= {arXiv preprint arXiv:1604.06042},
year = {2016}
}