Higher codimension relative isoperimetric inequality outside a convex set

2017/10/13 by Krummel, Brian · 1 citation
#49Q20 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1710.04821

Abstract

We consider an isoperimetric inequality for (m+1)-dimensional area minimizing submanifolds of arbitrary codimension which lie outside a convex set K ⊂ ℝⁿ⁺¹ and are bounded by a submanifold of ℝⁿ⁺¹ ∖ K and the convex set K. We show that the least value of the isoperimetric ratio is attained for an (m+1)-dimensional flat half-disk of ℝⁿ⁺¹₊. This extends prior work of Choe, Ghomi, and Ritoré in codimension one and proves a conjecture of Choe in the case of relative area minimizers.

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