Mountain Pass Theorem With infinite symmetry
Noe Barcenas
TL;DR
This paper extends the Mountain Pass Theorem to functionals invariant under infinite discrete groups with specific symmetry conditions, broadening its applicability in variational problems.
Contribution
It introduces a generalized version of the Mountain Pass Theorem accommodating infinite discrete group symmetries under a maximality condition.
Findings
Extended Mountain Pass Theorem for infinite symmetries
Applicable to broader classes of variational problems
Provides new tools for symmetric critical point theory
Abstract
We extend a work of Bartsch, Clapp and Puppe on the Mountain pass theorems. We consider functionals invariant with respect to infinite discrete groups satisfying a maximality condition on the finite subgroups.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology