DEFORMING SOLUTIONS OF GEOMETRIC VARIATIONAL PROBLEMS WITH VARYING SYMMETRY GROUPS |
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Authors: | R G BETTIOL P PICCIONE G SICILIANO |
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Institution: | 1. Department of Mathematics, University of Notre Dame, 255 Hurley Building, Notre Dame, IN, 46556-4618, USA 2. Departamento de Matemática, Universidade de S?o Paulo, Rua do Mat?o, 1010, S?o Paulo, SP, 05508-090, Brazil
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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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