On the topology and index of minimal surfaces

Otis Chodosh; Davi Maximo

doi:10.4310/jdg/1478138547

On the topology and index of minimal surfaces

Otis Chodosh, Davi Maximo

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We show that for an immersed two-sided minimal surface in R³, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R³ of index 2, as conjectured by Choe [4]. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface.

Original language	English (US)
Pages (from-to)	399-418
Number of pages	20
Journal	Journal of Differential Geometry
Volume	104
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1478138547
State	Published - Nov 2016

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

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10.4310/jdg/1478138547

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abstract = "We show that for an immersed two-sided minimal surface in R3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R3 of index 2, as conjectured by Choe [4]. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface.",

author = "Otis Chodosh and Davi Maximo",

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AB - We show that for an immersed two-sided minimal surface in R3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R3 of index 2, as conjectured by Choe [4]. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface.

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On the topology and index of minimal surfaces

Abstract

All Science Journal Classification (ASJC) codes

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