The isoperimetric inequality for a minimal submanifold in Euclidean space

2019/07/22 by Simon Brendle, Brendle, S. · 6 citations
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1907.09446

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.

Citations

• Normal and Integral Currents

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• Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds
• Minimal surfaces and comparison geometry
• An Isoperimetric-Type Inequality for Spacelike Submanifold in the Minkowski Space

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