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arXiv · 1608.05541

Complex Legendre duality

Bo Berndtsson·Dario Cordero-Erausquin·Bo'az Klartag·Yanir A. Rubinstein
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Abstract

We introduce complex generalizations of the classical Legendre transform, operating on Kähler metrics on a compact complex manifold. These Legendre transforms give explicit local isometric symmetries for the Mabuchi metric on the space of Kähler metrics around any real analytic Kähler metric, answering a question originating in Semmes' work.

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Bo Berndtsson, Dario Cordero-Erausquin, Bo'az Klartag, Yanir A. Rubinstein. 2016-08-19. Complex Legendre duality. https://doi.org/10.1353/ajm.2020.0008

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