Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone
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 questio...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
25.05.2017
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.1705.09122 |