Complex legendre duality
Journal article, 2020

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.


Bo Berndtsson

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Dario Cordero-Erausquin

Pierre and Marie Curie University (UPMC)

Bo’Az Klartag

Tel Aviv University

Weizmann Institute of Science

Yanir A. Rubinstein

University of Maryland

American Journal of Mathematics

0002-9327 (ISSN) 1080-6377 (eISSN)

Vol. 142 1 323-339

Subject Categories

Algebra and Logic


Mathematical Analysis



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