On Equivariant Morse Theory and Minimax Principles for Locally Lipschitz Maps

Lucas Fresse () and Viorica V. Motreanu ()
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Lucas Fresse: Institut Élie Cartan, Université de Lorraine
Viorica V. Motreanu: Lycée Varoquaux

Chapter 11 in Convex and Variational Analysis with Applications, 2026, pp 195-230 from Springer

Abstract: 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.

Keywords: Locally Lipschitz maps; Deformation theorems; Critical groups; Equivariant Morse theory; Homological linking; Homotopical linking; Minimax principles (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-032-07860-5_11

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DOI: 10.1007/978-3-032-07860-5_11

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