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On Equivariant Morse Theory and Minimax Principles for Locally Lipschitz Maps

Author

Listed:
  • Lucas Fresse

    (Institut Élie Cartan, Université de Lorraine)

  • Viorica V. Motreanu

    (Lycée Varoquaux)

Abstract

We give new versions of the first and the second deformation theorems in the context of invariant locally Lipschitz maps on a real Banach space endowed with an isometric representation of a compact topological group. As an application of the second deformation result, we define equivariant critical groups for locally Lipschitz maps, extend standard results of Morse theory, and obtain, as a byproduct, existence and multiplicity results for critical orbits, involving in particular a notion of equivariant homological linking of pairs. As an application of the first deformation result, we establish a general minimax principle based on a notion of equivariant homotopical linking of pairs.

Suggested Citation

  • Lucas Fresse & Viorica V. Motreanu, 2026. "On Equivariant Morse Theory and Minimax Principles for Locally Lipschitz Maps," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-3-032-07860-5_11
    DOI: 10.1007/978-3-032-07860-5_11
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