Complex interpolation of R-norms, duality and foliations
Journal article, 2020

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.

Complex interpolation

Convex geometry


Bo Berndtsson

Chalmers, Mathematical Sciences, Algebra and geometry

Dario Cordero-Erausquin

Pierre and Marie Curie University (UPMC)

Bo’Az Klartag

Tel Aviv University

Yanir A. Rubinstein

University of Maryland

Journal of the European Mathematical Society

1435-9855 (ISSN) 1435-9863 (eISSN)

Vol. 22 2 477-505

Subject Categories

Computational Mathematics


Mathematical Analysis



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