Diastatic entropy and rigidity of complex hyperbolic manifolds

Roberto Mossa. "Diastatic entropy and rigidity of complex hyperbolic manifolds." Complex Manifolds 3.1 (2016): 186-192. <http://eudml.org/doc/277093>.

@article{RobertoMossa2016,
abstract = {Let 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.},
author = {Roberto Mossa},
journal = {Complex Manifolds},
keywords = {compact real analytic Kähler manifolds; compact complex hyperbolic manifolds},
language = {eng},
number = {1},
pages = {186-192},
title = {Diastatic entropy and rigidity of complex hyperbolic manifolds},
url = {http://eudml.org/doc/277093},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Roberto Mossa
TI - Diastatic entropy and rigidity of complex hyperbolic manifolds
JO - Complex Manifolds
PY - 2016
VL - 3
IS - 1
SP - 186
EP - 192
AB - Let 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.
LA - eng
KW - compact real analytic Kähler manifolds; compact complex hyperbolic manifolds
UR - http://eudml.org/doc/277093
ER -