Regularity of free boundary minimal surfaces in locally polyhedral domains. (English) Zbl 1498.49076
The authors consider the regularity of free-boundary minimal surfaces \(M\) inside some given domain \(\Omega\). Under a \(C^2\) regularity assumption on \(\partial \Omega\), Grüter and Jost [M. Grüter and J. Jost, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 13, 129–169 (1986; Zbl 0615.49018)] proved an Allard-type regularity theorem stating that if \(M\) is sufficiently varifold close to a free-boundary plane, then nearby \(M\) is a \(C^{1,\alpha}\) graph over such a plane. In the current paper, the authors investigate whether a similar property holds when \(\Omega\) is only piecewise \(C^2\) regular, refer to Theorem 1.1. Their results also recover known results for wedges.
Reviewer: Giorgio Saracco (Trento)
MSC:
| 49Q05 | Minimal surfaces and optimization |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
Citations:
Zbl 0615.49018References:
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