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arXiv · 1806.04665

Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold

Paul Laurain·Romain Petrides
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Abstract

We perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min-max value over all disk sweepouts of a manifold whose boundary lie in a submanifold. Our result is based on a proof of the convexity of the energy for free boundary harmonic maps and a generalization of Colding-Minicozzi replacement procedure.

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Paul Laurain, Romain Petrides. 2018-06-12. Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold. https://arxiv.org/abs/1806.04665

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