ENTROPY RIGIDITY OF SYMMETRIC SPACES WITHOUT FOCAL POINTS

被引:2
作者
Ledrappier, Francois [1 ]
Shu, Lin [2 ]
机构
[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
[2] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China
关键词
Volume entropy; rank one manifolds; NEGATIVE CURVATURE; HARMONIC-FUNCTIONS; CONJUGATE-POINTS; BROWNIAN-MOTION; GEODESIC-FLOW; MANIFOLDS; GEOMETRY; THEOREM;
D O I
10.1090/S0002-9947-2014-06016-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We characterize symmetric spaces without focal points by the equality case of general inequalities between geometric quantities.
引用
收藏
页码:3805 / 3820
页数:16
相关论文
共 33 条
[1]   POSITIVE HARMONIC-FUNCTIONS ON COMPLETE MANIFOLDS OF NEGATIVE CURVATURE [J].
ANDERSON, MT ;
SCHOEN, R .
ANNALS OF MATHEMATICS, 1985, 121 (03) :429-461
[2]  
BALLMANN W, 1987, J DIFFER GEOM, V25, P1
[3]  
BALLMANN W, 1989, FORUM MATH, V1
[4]  
Ballmann Werner, 1995, DMV SEMINAR, V25
[5]  
Benoist Y, 1992, Journal of the American Mathematical Society, V5, P33, DOI DOI 10.2307/2152750.MR1124979
[6]   ENTROPIES AND RIGIDITIES OF LOCALLY SYMMETRICAL SPACES WITH STRICTLY NEGATIVE CURVATURE [J].
BESSON, G ;
COURTOIS, G ;
GALLOT, S .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 1995, 5 (05) :731-799
[7]   VOLUME AND MINIMAL ENTROPY OF LOCALLY SYMMETRICAL SPACES [J].
BESSON, G ;
COURTOIS, G ;
GALLOT, S .
INVENTIONES MATHEMATICAE, 1991, 103 (02) :417-445
[8]   VISIBILITY MANIFOLDS [J].
EBERLEIN, P ;
ONEILL, B .
PACIFIC JOURNAL OF MATHEMATICS, 1973, 46 (01) :45-109
[9]  
Eschenburg Jost-Hinrich, 1977, MATH Z, V153, P237
[10]   ASYMPTOTICALLY HARMONIC COMPACT MANIFOLDS [J].
FOULON, P ;
LABOURIE, F .
INVENTIONES MATHEMATICAE, 1992, 109 (01) :97-111