Energy functionals and soliton equations for G sub(2)-forms

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. I...

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 42; no. 4; pp. 585 - 610
Main Authors Weiss, Hartmut, Witt, Frederik
Format Journal Article
LanguageEnglish
Published 01.12.2012
Subjects
Deformation
Dirichlet problem
Energy flow
Functionals
Mathematical analysis
Solitons
Stability
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Summary: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 G sub(2)-structures satisfy this soliton equation and study their infinitesimal soliton deformations.
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ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-012-9328-y