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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| Online Access | Get full text |
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| 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. |
|---|---|
| AbstractList | 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. |
| Author | Pasquarelli, Franco Bellettini, Giovanni Paolini, Maurizio |
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| BackLink | https://doi.org/10.48550/arXiv.1705.09122$$DView paper in arXiv |
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| Snippet | 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... |
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| SubjectTerms | Mathematics - Differential Geometry Mathematics - Geometric Topology |
| Title | Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone |
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