Preprint 2/2012

Mean-convex sets and minimal barriers

Emanuele Spadaro

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Submission date: 06. Jan. 2012
Pages: 25
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Abstract:
A mean-convex set can be regarded as a barrier for the construction of minimal surfaces. Namely, if Ω 3 is mean-convex and Γ Ω is a null-homotopic (in Ω) Jordan curve, then there exists an embedded minimal disk Σ Ω with boundary Γ. Does a mean-convex set Ω contain all minimal disks with boundary on Ω? Does it contain the solutions of Plateau’s problem? We answer this question negatively and characterize the least barrier enclosing all the minimal hypersurfaces with boundary on a given set.

21.02.2013, 01:43