Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone

Maurizio Paolini, Franco Pasquarelli, Giovanni Bellettini

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

1 Citazioni (Scopus)

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 originaleEnglish
pagine (da-a)407-436
Numero di pagine30
RivistaInterfaces and Free Boundaries
DOI
Stato di pubblicazionePubblicato - 2018

Keywords

  • covers
  • minimal surfaces
  • soap films

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