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- Title
Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone.
- Authors
BELLETTINI, GIOVANNI; PAOLINI, MAURIZIO; PASQUARELLI, FRANCO
- Abstract
By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. 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 surface of positive genus spanning the boundary of an elongated tetrahedron and having area strictly less than the area of the conic surface.
- Subjects
COVERING spaces (Topology); PLATEAU'S problem; TETRAHEDRA; FUNCTIONS of bounded variation; SET theory
- Publication
Interfaces & Free Boundaries, 2018, Vol 20, Issue 3, p407
- ISSN
1463-9963
- Publication type
Article
- DOI
10.4171/IFB/407