71 citations · 404 across the 38 of their papers we have counts for
38 papers
-polarity, Mahler volumes, and the isotropic constant
Bo Berndtsson, Vlassis Mastrantonis, Yanir A. Rubinstein
This article introduces versions of the support function of a convex body and associates to these canonical -polar bodies and Mahler volumes $\mathcal…
Plurisubharmonic functions and real submanifolds of $\C^n$
Bo Berndtsson
We give an estimate for the volume of an analytic variety (or more generally the mass of a positive closed current) close to a real submanifold . Applications are given to the H…
Long geodesics in the space of Kähler metrics
Bo Berndtsson
We give some remarks on geodesics in the space of Kähler metrics that are defined for all time. Such curves are conjecturally induced by holomorphic vector fields, and we show that…
Bergman kernels for Paley-Wiener spaces and Nazarov's proof of the Bourgain-Milman theorem
Bo Berndtsson
We give a general inequality for Bergman kernels of Bergman spaces defined by convex weights in $\C^n$. We also discuss how this can be used in Nazarov's proof of the Bourgain-Milm…
Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem
Bo Berndtsson
We give a proof of the Bourgain-Milman theorem using complex methods. The proof is inspired by Kuperberg's, but considerably shorter.
Complex Brunn-Minkowski theory and positivity of vector bundles
Bo Berndtsson
This is a survey of results on positivity of vector bundles, inspired by the Brunn-Minkowski and Prékopa theorems. Applications to complex analysis, Kähler geometry and algebraic g…