The Existence of Three Short Closed Geodesics

1985 ◽  
pp. 169-179
Author(s):  
Wilhelm Klingenberg
Keyword(s):  
Closed Geodesics

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

scholarly journals A central limit theorem for random closed geodesics: Proof of the Chas–Li–Maskit conjecture

2019 ◽  
Vol 358 ◽  
pp. 106852
Author(s):  
Ilya Gekhtman ◽  
Samuel J. Taylor ◽  
Giulio Tiozzo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Closed Geodesics

scholarly journals Angular self-intersections for closed geodesics on surfaces

2005 ◽  
Vol 134 (02) ◽  
pp. 419-426 ◽  
Author(s):  
Mark Pollicott ◽  
Richard Sharp
Keyword(s):  
Closed Geodesics

scholarly journals Closed geodesics and bounded gaps

2016 ◽  
Vol 287 (1-2) ◽  
pp. 547-554
Author(s):  
Anton Deitmar
Keyword(s):  
Closed Geodesics ◽  
Bounded Gaps

scholarly journals A Viscosity method for the min-max construction of closed geodesics

2016 ◽  
Vol 22 (4) ◽  
pp. 1282-1324 ◽  
Author(s):  
Alexis Michelat ◽  
Tristan Rivière
Keyword(s):  
Closed Geodesics ◽  
Viscosity Method

Closed Geodesics on Riemann Surfaces

1978 ◽  
Vol 72 (1) ◽  
pp. 140 ◽  
Author(s):  
Troels Jorgensen
Keyword(s):  
Riemann Surfaces ◽  
Closed Geodesics

scholarly journals ESTIMATES AND COMPUTATIONS IN RABINOWITZ–FLOER HOMOLOGY

2009 ◽  
Vol 01 (04) ◽  
pp. 307-405 ◽  
Author(s):  
ALBERTO ABBONDANDOLO ◽  
MATTHIAS SCHWARZ
Keyword(s):  
Maximum Principle ◽  
Energy Level ◽  
Exact Sequence ◽  
Floer Homology ◽  
Energy Functional ◽  
Convex Compact ◽  
Closed Geodesics ◽  
Action Functional ◽  
Uniform Estimates ◽  
Rabinowitz Floer Homology

The Rabinowitz–Floer homology of a Liouville domain W is the Floer homology of the Rabinowitz free period Hamiltonian action functional associated to a Hamiltonian whose zero energy level is the boundary of W. This invariant has been introduced by K. Cieliebak and U. Frauenfelder and has already found several applications in symplectic topology and in Hamiltonian dynamics. Together with A. Oancea, the same authors have recently computed the Rabinowitz–Floer homology of the cotangent disk bundle D* M of a closed Riemannian manifold M, by means of an exact sequence relating the Rabinowitz–Floer homology of D* M with its symplectic homology and cohomology. The first aim of this paper is to present a chain level construction of this exact sequence. In fact, we show that this sequence is the long homology sequence induced by a short exact sequence of chain complexes, which involves the Morse chain complex and the Morse differential complex of the energy functional for closed geodesics on M. These chain maps are defined by considering spaces of solutions of the Rabinowitz–Floer equation on half-cylinders, with suitable boundary conditions which couple them with the negative gradient flow of the geodesic energy functional. The second aim is to generalize this construction to the case of a fiberwise uniformly convex compact subset W of T* M whose interior part contains a Lagrangian graph. Equivalently, W is the energy sublevel associated to an arbitrary Tonelli Lagrangian L on TM and to any energy level which is larger than the strict Mañé critical value of L. In this case, the energy functional for closed geodesics is replaced by the free period Lagrangian action functional associated to a suitable calibration of L. An important issue in our analysis is to extend the uniform estimates for the solutions of the Rabinowitz–Floer equation — both on cylinders and on half-cylinders — to Hamiltonians which have quadratic growth in the momenta. These uniform estimates are obtained by the Aleksandrov integral version of the maximum principle. In the case of half-cylinders, they are obtained by an Aleksandrov-type maximum principle with Neumann conditions on part of the boundary.

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