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.
Scheda prodotto non validato
Scheda prodotto in fase di analisi da parte dello staff di validazione
|Titolo:||Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone|
|Appare nelle tipologie:||1.1 Articolo in rivista|
File in questo prodotto: