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On the stability of the CMC Clifford Tori as constrained Willmore surfaces

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Abstract

The tori \({T_r = r\, \mathbb{S}^1 \times s\mathbb{S}^1 \subset \mathbb{S}^3}\), where r 2 + s 2 = 1 are constrained Willmore surfaces, i.e., critical points of the Willmore functional among tori of the same conformal type. We compute which of the T r are stable critical points.

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  1. Mathematisches Institut, Universität Freiburg, Eckerstraße 1, 79104, Freiburg, Germany

    Ernst Kuwert & Johannes Lorenz

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  1. Ernst Kuwert
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  2. Johannes Lorenz
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Correspondence to Johannes Lorenz.

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Kuwert, E., Lorenz, J. On the stability of the CMC Clifford Tori as constrained Willmore surfaces. Ann Glob Anal Geom 44, 23–42 (2013). https://doi.org/10.1007/s10455-012-9354-9

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  • DOI: https://doi.org/10.1007/s10455-012-9354-9

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