Simple closed geodesics and the study of Teichmüller spaces

2014 ◽  
pp. 113-134 ◽  
Author(s):  
Hugo Parlier
Keyword(s):  
Closed Geodesics ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Simple Closed Geodesics

Holomorphic Motions and Teichmuller Spaces

1994 ◽  
Vol 343 (2) ◽  
pp. 927 ◽  
Author(s):  
C. J. Earle ◽  
I. Kra ◽  
S. L. Krushkal'
Keyword(s):  
Teichmüller Spaces ◽  
Holomorphic Motions ◽  
Teichmuller Spaces

SHARP POINCARÉ–SOBOLEV INEQUALITIES AND THE SHORTEST LENGTH OF SIMPLE CLOSED GEODESICS ON A TOPOLOGICAL TWO SPHERE

2004 ◽  
Vol 06 (05) ◽  
pp. 781-792 ◽  
Author(s):  
MEIJUN ZHU
Keyword(s):  
Riemannian Manifold ◽  
Sobolev Inequalities ◽  
Square Root ◽  
Two Dimensional ◽  
Closed Geodesics ◽  
Sharp Constants ◽  
Simple Closed Geodesics

We show that the sharp constants of Poincaré–Sobolev inequalities for any smooth two dimensional Riemannian manifold are less than or equal to [Formula: see text]. For a smooth topological two sphere M2, the sharp constants are [Formula: see text] if and only if M2 is isometric to two sphere S2 with the standard metric. In the same spirit, we show that for certain special smooth topological sphere the ratio between the shortest length of simple closed geodesics and the square root of its area is less than or equals to [Formula: see text].

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