A direct approach to Plateau's problem in any codimension

G. De Philippis; A. De Rosa; F. Ghiraldin

doi:10.1016/j.aim.2015.10.007

A direct approach to Plateau's problem in any codimension

G. De Philippis, A. De Rosa, F. Ghiraldin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also show that the obtained minimizers are regular up to a set of dimension less than (d-1).

Original language	English (US)
Pages (from-to)	59-80
Number of pages	22
Journal	Advances in Mathematics
Volume	288
DOIs	https://doi.org/10.1016/j.aim.2015.10.007
State	Published - Jan 22 2016

Keywords

Geometric measure theory
Plateau's problem
Rectifiable sets

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2015.10.007

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abstract = "This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also show that the obtained minimizers are regular up to a set of dimension less than (d-1).",

keywords = "Geometric measure theory, Plateau's problem, Rectifiable sets",

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AU - Ghiraldin, F.

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AB - This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also show that the obtained minimizers are regular up to a set of dimension less than (d-1).

KW - Geometric measure theory

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KW - Rectifiable sets

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A direct approach to Plateau's problem in any codimension

Abstract

Keywords

ASJC Scopus subject areas

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