Splitting lemmas for the Finsler energy functional on the space ofH1-curves

DOI10.1112/plms/pdw022zbMath1406.58007arXiv1411.3209OpenAlexW2963915068WikidataQ124992720 ScholiaQ124992720MaRDI QIDQ2827962

Guang-Cun Lu

Publication date: 24 October 2016

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3209

zbMATH Keywords

Hilbert manifoldsMorse lemmasFinsler metric, energy functional

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (3)

The Morse index theorem in the case of two variable endpoints in conic Finsler manifolds ⋮ Morse theory methods for a class of quasi-linear elliptic systems of higher order ⋮ Parameterized splitting theorems and bifurcations for potential operators. I: Abstract theory

Cites Work

• Unnamed Item
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• On the existence of infinitely many invariant Reeb orbits
• String homology, and closed geodesics on manifolds which are elliptic spaces
• The splitting lemmas for nonsmooth functionals on Hilbert spaces. I.
• On the multiplicity of isometry-invariant geodesics on product manifolds
• Isometries, submetries and distance coordinates on Finsler manifolds
• Methods of infinite dimensional Morse theory for geodesics on Finsler manifolds
• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• Corrigendum to ``The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems
• Local Floer homology and infinitely many simple Reeb orbits
• The principle of symmetric criticality
• Elliptic isometries, condition (C) and proper maps
• High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
• Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric
• Functional analysis, Sobolev spaces and partial differential equations
• Metrics with only finitely many isometry invariant geodesics
• Isometry-invariant geodesics on spheres
• The rational homotopy theory of certain path spaces with applications to geodesics
• On the existence of infinitely many isometry-invariant geodesics
• Critical point theory and submanifold geometry
• The homology theory of the closed geodesic problem
• On the number of invariant closed geodesics
• Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesics
• Contributions of rational homotopy theory to global problems in geometry
• Isometry-invariant geodesics
• The group of isometries of a Finsler space.
• The geometry of Lagrange spaces: theory and applications
• Isometry-invariant geodesics and the fundamental group
• Addendum to ``Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric
• Isometry-invariant geodesics and nonpositive derivations of the cohomology
• Homotopy theory of infinite dimensional manifolds
• Periodic geodesics on compact Riemannian manifolds
• On differentiable functions with isolated critical points
• Geodesics and Jacobi fields of pseudo-Finsler manifolds
• The index of a geodesic in a Randers space and some remarks about the lack of regularity of the energy functional of a Finsler metric
• On the Free Loop Space of Homogeneous Spaces
• Differential Topology
• On invariant closed geodesics under isometries
• Chern connection of a pseudo-Finsler metric as a family of affine connections
• Corrigendum to ``Chern connection of a pseudo-Finsler metric as a family of affine connections"
• Local contact homology and applications
• Rational Homotopy Theory II
• Lagrange geometry
• On the Banach differential structure for sets of maps on non-compact domains

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