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.

Paolini, M., Pasquarelli, F., Bellettini, G., Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone, <<INTERFACES AND FREE BOUNDARIES>>, 2018; (20): 407-436. [doi:10.4171/IFB/407] [http://hdl.handle.net/10807/126867]

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

Paolini, Maurizio;Pasquarelli, Franco;
2018

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.
Inglese
Paolini, M., Pasquarelli, F., Bellettini, G., Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone, <<INTERFACES AND FREE BOUNDARIES>>, 2018; (20): 407-436. [doi:10.4171/IFB/407] [http://hdl.handle.net/10807/126867]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/126867
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