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

Vanderson Lima, Ana Menezes

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 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.

Original languageEnglish (US)
Pages (from-to)1661-1686
Number of pages26
JournalTransactions of the American Mathematical Society
Volume374
Issue number3
DOIs
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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