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On Berndtsson's generalization of Prekopa's theorem

Abstract : We present a new approach to Berndtsson's complex extension of Prekopa's theorem. This approach is inspired by the recent local proof of Prekopa's theorem obtained by Ball, Barthe and Naor. In the complex setting, this approach leads to a formula expressing DeltaPhi in terms of (derivatives of)omega where e(-Phi(z)) = integrale(-phi(z,w)) dlambda(w) As a consequence, we obtain new conditions ensuring that Phi is subharmonic when phi is plurisubharmonic.
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Submitted on : Tuesday, May 1, 2012 - 8:19:39 PM
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Dario Cordero-Erausquin. On Berndtsson's generalization of Prekopa's theorem. Mathematische Zeitschrift, Springer, 2005, 249 (2), pp.401--410. ⟨10.1007/s00209-004-0704-6⟩. ⟨hal-00693111⟩



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