Some Properties of the Intersection of Free Boundary Minimal Hypersurfaces in Euclidean Balls

Barbosa, Ezequiel; Carvalho, Alcides de; Santos, Roney Lira de Sales

doi:10.48550/arxiv.2109.13007

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“…After we had announced our result in talks on the last months, it came to our knowledge that Theorem A was also obtained by Barbosa, Carvalho and Santos [5]. Their technique is different from ours and is based on a tangency principle.…”

Section: Introductionmentioning

confidence: 77%

A two-piece property for free boundary minimal surfaces in the ball

Lima¹,

Menezes²

2020

Trans. Amer. Math. Soc.

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We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 3 3 -ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Moreover, we prove the regularity at the corners of currents minimizing a partially free boundary problem by following ideas by Grüter and Simon. Our first result gives evidence to a conjecture by Fraser and Li.

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Section: Introductionmentioning

confidence: 77%