Commentarii Mathematici Helvetici


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Volume 83, Issue 3, 2008, pp. 539–546
DOI: 10.4171/CMH/135

Published online: 2008-09-30

Relating diameter and mean curvature for submanifolds of Euclidean space

Peter Topping[1]

(1) University of Warwick, Coventry, United Kingdom

Given a closed m-dimensional manifold ℳ  immersed in ℝn, we estimate its diameter d in terms of its mean curvature H by

dC(m) ℳ  |H|m − 1 .

Keywords: Geometric inequalities, diameter, mean curvature, volume, Michael–Simon Sobolev inequalities, geometric maximal function

Topping Peter: Relating diameter and mean curvature for submanifolds of Euclidean space. Comment. Math. Helv. 83 (2008), 539-546. doi: 10.4171/CMH/135