Closed geodesics on surfaces without conjugate points

Vaughn Climenhaga, Gerhard Knieper, Khadim War

Type: Article

Publication Date: 2021-08-21

Citations: 5

DOI: https://doi.org/10.1142/s021919972150067x

Abstract

We obtain Margulis-type asymptotic estimates for the number of free homotopy classes of closed geodesics on certain manifolds without conjugate points. Our results cover all compact surfaces of genus at least 2 without conjugate points.

Locations

arXiv (Cornell University) - View - PDF
Communications in Contemporary Mathematics - View

Similar Works

Action	Title	Year	Authors
+	Closed geodesics on surfaces without conjugate points	2020	Vaughn Climenhaga Gerhard Knieper Khadim War
+	Closed geodesics on surfaces without conjugate points	2020	Vaughn Climenhaga Gerhard Knieper Khadim War
+	Counting geodesic loops on surfaces of genus at least 2 without conjugate points	2023	Mark Pollicott Khadim War
+	On the existence of infinitely many closed geodesics on non-compact manifolds	2016	Luca Asselle Marco Mazzucchelli
+	Closed geodesics with local homology in maximal degree on non-compact manifolds	2017	Luca Asselle Marco Mazzucchelli
+ PDF Chat	Geodesics and ends in certain surfaces without conjugate points	1978	Patrick Eberlein
+	Prime geodesic theorem and closed geodesics for large genus	2022	Yunhui Wu Yuhao Xue
+ PDF Chat	Counting closed geodesics in moduli space	2011	Alex Eskin Maryam Mirzakhani
+ PDF Chat	Closed geodesics on hyperbolic surfaces with few intersections	2024	Wujie Shen
+	Simple closed geodesics on most Alexandrov surfaces	2013	Joël Rouyer Costin Vîlcu
+	Simple closed geodesics on most Alexandrov surfaces	2013	Joël Rouyer Costin Vîlcu
+	Simple closed geodesics on most Alexandrov surfaces	2015	Joël Rouyer Costin Vîlcu
+ PDF Chat	Density of expansivity for geodesic flows of compact higher genus surfaces without conjugate points	2024	Edhin Franklin Mamani Rafael O. Ruggiero
+ PDF Chat	Lower bound on the number of non-simple closed geodesics on surfaces	2016	Jenya Sapir
+ PDF Chat	A central limit theorem for random closed geodesics: Proof of the Chas–Li–Maskit conjecture	2019	Ilya Gekhtman S. J. Taylor Giulio Tiozzo
+ PDF Chat	On the multiplicity of the image of simple closed curves via holomorphic maps between compact Riemann surfaces	2003	H. Yamamoto
+	Geodesics with one self-intersection, and other stories	2012	Igor Rivin
+	Mirzakhani’s frequencies of simple closed geodesics on hyperbolic surfaces in large genus and with many cusps	2025	Irene Ren
+	Closed geodesics on surfaces of genus 0	1979	Wilhelm Klingenberg
+	Families of closed geodesics on hyperbolic surfaces with common self-intersections	1994	Thea Pignataro Hanna Sandler

Works That Cite This (5)

Action	Title	Year	Authors
+	Unique ergodicity of horocyclic flows on nonpositively curved surfaces	2024	Sergi Burniol Clotet
+ PDF Chat	On the equidistribution of closed geodesics and geodesic nets	2023	Xinze Li Bruno Staffa
+	Volume asymptotics, Margulis function and rigidity beyond nonpositive curvature	2023	Weisheng Wu
+ PDF Chat	Anatole Katok	2021	Boris Hasselblatt
+ PDF Chat	Unique ergodicity of the horocycle flow of a higher genus compact surface with no conjugate points and continuous Green bundles	2023	Sergi Burniol Clotet

Works Cited by This (31)

Action	Title	Year	Authors
+ PDF Chat	On surfaces with no conjugate points	1987	Werner Ballmann Michael Brin Keith Burns
+ PDF Chat	The length spectra of some compact manifolds of negative curvature	1977	Ramesh Gangolli
+ PDF Chat	On the variety of manifolds without conjugate points	1975	Robert Gulliver
+ PDF Chat	The limit set of a Fuchsian group	1976	S. J. Patterson
+	Growth of conjugacy classes in Gromov hyperbolic groups	2002	Michel Coornaert Gerhard Knieper
+ PDF Chat	Geodesic flow on the two-sphere, Part I: Positive measure entropy	1988	Victor J. Donnay
+ PDF Chat	Geodesic flow in certain manifolds without conjugate points	1972	Patrick Eberlein
+	An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a Flows	1983	William Parry Mark Pollicott
+ PDF Chat	Mesures de Patterson-Sullivan sur le bord d’un espace hyperbolique au sens de Gromov	1993	Michel Coornaert
+	Selberg's trace formula as applied to a compact riemann surface	1972	H. P. McKean