Complex interpolation of R-norms, duality and foliations

Bo Berndtsson, Dario Cordero-Erausquin, Bo’az Klartag, Yanir A. Rubinstein

Research output: Contribution to journalArticlepeer-review

Abstract

The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Słodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge–Ampère equation.

Original languageEnglish
Pages (from-to)477-505
Number of pages29
JournalJournal of the European Mathematical Society
Volume22
Issue number2
DOIs
StatePublished - 2020

Funding

FundersFunder number
National Science Foundation
American Institute of Mathematics

    Keywords

    • Complex interpolation
    • Convex geometry

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