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Energy functionals and soliton equations for G2-forms

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Abstract

We extend short-time existence and stability of the Dirichlet energy flow as proven in a previous article by the authors to a broader class of energy functionals. Furthermore, we derive some monotonely decreasing quantities for the Dirichlet energy flow and investigate an equation of soliton type. In particular, we show that nearly parallel G2-structures satisfy this soliton equation and study their infinitesimal soliton deformations.

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Authors and Affiliations

  1. Mathematisches Institut der LMU München, Theresienstrasse 39, 80333, München, Germany

    Hartmut Weiss

  2. Mathematisches Institut der Universität Münster, Einsteinstrasse 62, 48149, Münster, Germany

    Frederik Witt

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  1. Hartmut Weiss
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  2. Frederik Witt
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Correspondence to Hartmut Weiss.

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Weiss, H., Witt, F. Energy functionals and soliton equations for G2-forms. Ann Glob Anal Geom 42, 585–610 (2012). https://doi.org/10.1007/s10455-012-9328-y

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  • DOI: https://doi.org/10.1007/s10455-012-9328-y

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