JournalscmhVol. 83 , No. 3DOI 10.4171/cmh/135

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

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 .