JournalscmhVol. 83, No. 3pp. 539–546

Relating diameter and mean curvature for submanifolds of Euclidean space

  • Peter Topping

    University of Warwick, Coventry, United Kingdom
Relating diameter and mean curvature for submanifolds of Euclidean space cover
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Abstract

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

d ≤ C(m) ∫ℳ  |H|m − 1 dμ .

Cite this article

Peter Topping, Relating diameter and mean curvature for submanifolds of Euclidean space. Comment. Math. Helv. 83 (2008), no. 3, pp. 539–546

DOI 10.4171/CMH/135