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 language | English (US) |
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Pages (from-to) | 1661-1686 |
Number of pages | 26 |
Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2021 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics