Closed geodesics on surfaces without conjugate points

被引：5

作者：

Climenhaga, Vaughn ^{[1
]}

Knieper, Gerhard ^{[2
]}

War, Khadim ^{[3
]}

机构：

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

[2] Ruhr Univ Bochum, Dept Math, D-44780 Bochum, Germany

[3] IMPA, Estr Dona Castorina 110, Rio De Janeiro, Brazil

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2022年 / 24卷 / 06期

关键词：

Geodesic flows; no conjugate points; closed geodesics; equidistribution; Margulis asymptotics; MAXIMAL ENTROPY; PERIODIC-ORBITS; FLOWS; MANIFOLDS; GROWTH; UNIQUENESS;

D O I：

10.1142/S021919972150067X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：35

共 50 条

[31] The Hopf-Tsuji-Sullivan dichotomy on visibility manifolds without conjugate points
Liu, Fei
Liu, Xiaokai
Wang, Fang
JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 423 : 286 - 323
[32] Closed geodesics on orbifolds of nonpositive or nonnegative curvature
Dragomir, George C.
GEOMETRIAE DEDICATA, 2014, 172 (01) : 399 - 411
[33] CLOSED MAGNETIC GEODESICS ON S2
Schneider, Matthias
JOURNAL OF DIFFERENTIAL GEOMETRY, 2011, 87 (02) : 343 - 388
[34] THE FLAT STRIP THEOREM FAILS FOR SURFACES WITH NO CONJUGATE-POINTS
BURNS, K
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 115 (01) : 199 - 206
[35] SQUARE-INTEGRABILITY OF THE MIRZAKHANI FUNCTION AND STATISTICS OF SIMPLE CLOSED GEODESICS ON HYPERBOLIC SURFACES
Arana-Herrera, Francisco
Athreya, Jayadev S.
FORUM OF MATHEMATICS SIGMA, 2020, 8
[36] Closed geodesics with Lipschitz obstacle
Degiovanni, M
Morbini, L
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 233 (02) : 767 - 789
[37] Geodesics in Minimal Surfaces
Riveros, Carlos M. C.
Corro, Armando M. V.
MATHEMATICAL NOTES, 2017, 101 (3-4) : 497 - 514
[38] The Type Numbers of Closed Geodesics
Taimanov, I. A.
REGULAR & CHAOTIC DYNAMICS, 2010, 15 (01) : 84 - 100
[39] CLOSED GEODESICS ON REGULAR POLYHEDRA
Fuchs, Dmitry
Fuchs, Ekaterina
MOSCOW MATHEMATICAL JOURNAL, 2007, 7 (02) : 265 - 279
[40] Reversibility at infinity and rigidity of Finsler manifolds without conjugate points
Chimenton, Alessandro Gaio
Gomes, Jose Barbosa
Ruggiero, Rafael O. O.
GEOMETRIAE DEDICATA, 2023, 217 (02)

← 1 2 3 4 5 →