A Viscosity method for the min-max construction of closed geodesics
Autor: | Alexis Michelat, Tristan Rivière |
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Rok vydání: | 2016 |
Předmět: |
Mathematics - Differential Geometry
Pure mathematics Sequence Control and Optimization Geodesic 010102 general mathematics 53C22 58E10 34K13 49Q05 01 natural sciences Computational Mathematics Mathematics - Analysis of PDEs Differential Geometry (math.DG) Dimension (vector space) Control and Systems Engineering Viscosity (programming) 0103 physical sciences Convergence (routing) FOS: Mathematics Mathematics::Differential Geometry 010307 mathematical physics Finsler manifold 0101 mathematics Analysis of PDEs (math.AP) Mathematics |
Zdroj: | ESAIM: Control, Optimisation and Calculus of Variations. 22:1282-1324 |
ISSN: | 1262-3377 1292-8119 |
DOI: | 10.1051/cocv/2016039 |
Popis: | We present a viscosity approach to the min-max construction of closed geodesics on compact Riemannian manifolds of arbitrary dimension. The existence is proved in the case of surfaces, and reduced to a topological condition in general. We also construct counter-examples in dimension 1 and 2 to the e -regularity in the convergence procedure. Furthermore, we prove the lower semi-continuity of the index of our sequence of critical points converging towards a closed non-trivial geodesic. |
Databáze: | OpenAIRE |
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