On stability of equivariant minimal tori in the 3-sphere

M. Kilian; M. U. Schmidt; N. Schmitt

doi:10.1016/j.geomphys.2014.05.008

On stability of equivariant minimal tori in the 3-sphere

M. Kilian
, M. U. Schmidt
, N. Schmitt

School of Mathematical Sciences

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

Abstract

We prove that amongst the equivariant constant mean curvature tori in the 3-sphere, the Clifford torus is the only local minimum of the Willmore energy. All other equivariant minimal tori in the 3-sphere are local maxima of the Willmore energy.

Original language	English
Pages (from-to)	171-176
Number of pages	6
Journal	Journal of Geometry and Physics
Volume	85
DOIs	https://doi.org/10.1016/j.geomphys.2014.05.008
Publication status	Published - 2014

Keywords

Isoperiodic deformation
Minimal surfaces
Willmore energy

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10.1016/j.geomphys.2014.05.008

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title = "On stability of equivariant minimal tori in the 3-sphere",

abstract = "We prove that amongst the equivariant constant mean curvature tori in the 3-sphere, the Clifford torus is the only local minimum of the Willmore energy. All other equivariant minimal tori in the 3-sphere are local maxima of the Willmore energy.",

keywords = "Isoperiodic deformation, Minimal surfaces, Willmore energy",

author = "M. Kilian and Schmidt, \{M. U.\} and N. Schmitt",

year = "2014",

doi = "10.1016/j.geomphys.2014.05.008",

language = "English",

volume = "85",

pages = "171--176",

journal = "Journal of Geometry and Physics",

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T1 - On stability of equivariant minimal tori in the 3-sphere

AU - Kilian, M.

AU - Schmidt, M. U.

AU - Schmitt, N.

PY - 2014

Y1 - 2014

N2 - We prove that amongst the equivariant constant mean curvature tori in the 3-sphere, the Clifford torus is the only local minimum of the Willmore energy. All other equivariant minimal tori in the 3-sphere are local maxima of the Willmore energy.

AB - We prove that amongst the equivariant constant mean curvature tori in the 3-sphere, the Clifford torus is the only local minimum of the Willmore energy. All other equivariant minimal tori in the 3-sphere are local maxima of the Willmore energy.

KW - Isoperiodic deformation

KW - Minimal surfaces

KW - Willmore energy

UR - https://www.scopus.com/pages/publications/84955202150

U2 - 10.1016/j.geomphys.2014.05.008

DO - 10.1016/j.geomphys.2014.05.008

M3 - Article

AN - SCOPUS:84955202150

SN - 0393-0440

VL - 85

SP - 171

EP - 176

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

On stability of equivariant minimal tori in the 3-sphere

Abstract

Keywords

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