Header

UZH-Logo

Maintenance Infos

A direct approach to Plateau's problem in any codimension


De Philippis, Guido; De Rosa, Antonio; Ghiraldin, Francesco (2016). A direct approach to Plateau's problem in any codimension. Advances in Mathematics, 288:59-80.

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 $\mathit{d}$ -rectifiable closed subsets of $\mathbb{R}^{\mathit{n}}$: 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 ($\mathit{d}$−1).

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 $\mathit{d}$ -rectifiable closed subsets of $\mathbb{R}^{\mathit{n}}$: 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 ($\mathit{d}$−1).

Statistics

Citations

3 citations in Web of Science®
3 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

1 download since deposited on 12 Jan 2017
1 download since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:January 2016
Deposited On:12 Jan 2017 10:38
Last Modified:08 Dec 2017 22:11
Publisher:Elsevier
ISSN:0001-8708
Publisher DOI:https://doi.org/10.1016/j.aim.2015.10.007

Download

Content: Accepted Version
Language: English
Filetype: PDF - Registered users only until 23 January 2018
Size: 322kB
View at publisher
Embargo till: 2018-01-23