The isoperimetric inequality for a minimal submanifold in Euclidean space

Abstract

We prove a Sobolev inequality which holds on submanifolds in Euclidean space of arbitrary dimension and codimension. This inequality is sharp if the codimension is at most 2. As a special case, we obtain a sharp isoperimetric inequality for minimal submanifolds in Euclidean space of codimension at most 2.

final version, to appear in J Amer Math Soc

Cited by in corpus (3)

• Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces
• The Minkowski inequality in de Sitter space
• An Isoperimetric-Type Inequality for Spacelike Submanifold in the Minkowski Space