Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball

1980 ◽  
Vol 4 (5) ◽  
pp. 1011-1021 ◽  
Author(s):  
K. Goebel ◽  
T. Sekowski ◽  
A. Stachura
Keyword(s):  
Fixed Points ◽  
Hyperbolic Metric ◽  
Holomorphic Mappings ◽  
Uniform Convexity ◽  
The Hyperbolic Metric ◽  
Hilbert Ball

Approximating fixed points of holomorphic mappings in the Hilbert ball

2009 ◽  
Vol 70 (12) ◽  
pp. 4145-4150 ◽  
Author(s):  
Marina Levenshtein ◽  
Simeon Reich
Keyword(s):  
Fixed Points ◽  
Holomorphic Mappings ◽  
Hilbert Ball

scholarly journals Diastatic entropy and rigidity of complex hyperbolic manifolds

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Roberto Mossa
Keyword(s):  
Lower Bound ◽  
Hyperbolic Manifold ◽  
Hyperbolic Manifolds ◽  
Hyperbolic Metric ◽  
Continuous Map ◽  
The Hyperbolic Metric ◽  
Geometric Rigidity ◽  
Volume Entropy ◽  
Complex Hyperbolic Manifold ◽  
Real Analytic

AbstractLet f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary,when X = Y,we get that the minimal diastatic entropy is achieved if and only if g is isometric to the hyperbolic metric g0.

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