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.
Author
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 1 323-339Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1353/ajm.2020.0008