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. 539–546DOI 10.4171/CMH/135