Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds
Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds
Summary: Let \(M\) be a complete \(C^1\)-Finsler manifold without boundary and \(f: M\to \mathbb{R}\) be a locally Lipschitz function. The classical proof of the well-known deformation lemma can not be extended to this case because integral lines may not exist. In this paper, we establish existence of deformations generalizing the classical result. This allows us to prove some known results in a more general setting (minimax theorem, a theorem of Lyusternik-Schnirelman type, mountain pass theorem). This approach enables us to drop the compactness assumptions characteristic for recent papers in the field using the Ekeland's variational principle as the main tool.
- Institute of Mathematics and Informatics Bulgaria
- Bulgarian Academy of Sciences Bulgaria
C1–Finsler Manifold, Ljusternik-Schnirelmann Theory, locally Lipschitz function, theorem of Lyusternik-Schnirelman, Mountain Pass Theorem, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, 514, Locally Lipschitz Functions, mountain pass theorem, Deformation Lemma, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, minimax theorem, deformation lemma, \(C^ 1\)-Finsler manifold
C1–Finsler Manifold, Ljusternik-Schnirelmann Theory, locally Lipschitz function, theorem of Lyusternik-Schnirelman, Mountain Pass Theorem, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, 514, Locally Lipschitz Functions, mountain pass theorem, Deformation Lemma, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, minimax theorem, deformation lemma, \(C^ 1\)-Finsler manifold
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!