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arXiv · 1403.4275

Deforming solutions of geometric variational problems with varying symmetry groups

Renato G. Bettiol·Paolo Piccione·Gaetano Siciliano
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Abstract

We prove an equivariant implicit function theorem for variational problems that are invariant under a varying symmetry group (corresponding to a bundle of Lie groups). Motivated by applications to families of geometric variational problems lacking regularity, several non-smooth extensions of the result are discussed. Among such applications is the submanifold problem of deforming the ambient metric preserving a given variational property of a prescribed family of submanifolds, e.g., constant mean curvature, up to the action of the corresponding ambient isometry groups.

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Renato G. Bettiol, Paolo Piccione, Gaetano Siciliano. 2014-03-17. Deforming solutions of geometric variational problems with varying symmetry groups. https://doi.org/10.1007/s00031-014-9277-6

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