# Diastatic entropy and rigidity of complex hyperbolic manifolds

Complex Manifolds (2016)

- Volume: 3, Issue: 1, page 186-192
- ISSN: 2300-7443

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topRoberto 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 -

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