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Complex Legendre duality

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arxiv 1608.05541 v1 pith:RQFOIA34 submitted 2016-08-19 math.DG math.CV

Bo Berndtsson , Dario Cordero-Erausquin , Bo'az Klartag , Yanir A. Rubinstein This is my paper · ORCID
classification math.DGmath.CV
keywords ahlercomplexlegendremetricmetricsanalyticansweringaround
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We introduce complex generalizations of the classical Legendre transform, operating on K\"ahler metrics on a compact complex manifold. These Legendre transforms give explicit local isometric symmetries for the Mabuchi metric on the space of K\"ahler metrics around any real analytic K\"ahler metric, answering a question originating in Semmes' work.

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