On the diastatic entropy and C1-rigidity of complex hyperbolic manifolds
Abstract
Let f:(Y,g)->(X,g0) be a non zero degree continuous map between compact K\"ahler manifolds of dimension greater or equal to 2, where g0 has constant negative holomorphic sectional curvature. Adapting the Besson-Courtois-Gallot barycentre map techniques to the K\"ahler setting, we prove a gap theorem in terms of the degree of f and the diastatic entropies of (Y, g) and (X,g0), which extends the rigidity result proved by the author in [13].
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