Abstract
Using a suitable triple covering space it is possible to model the construction of a non-simply connected minimal surface spanning all six edges of an elongated tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. The possibility of using covering spaces for minimal surfaces was first proposed by Brakke. After a question raised by R. Hardt in the late 1980's, it seems common opinion that an area-minimizing surface of this sort does not exist for a regular tetrahedron, although a proof of this fact is still missing. In this paper we show that there exists a non-simply connected surface spanning the boundary of an elongated tetrahedron and having area strictly less than the area of the minimal contractible surface.
Lingua originale | Inglese |
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pagine (da-a) | 407-436 |
Numero di pagine | 30 |
Rivista | Interfaces and Free Boundaries |
Numero di pubblicazione | 20 |
DOI | |
Stato di pubblicazione | Pubblicato - 2018 |
All Science Journal Classification (ASJC) codes
- Superfici e Interfacce
Keywords
- covers
- minimal surfaces
- soap films