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Interpolations, Convexity and Geometric Inequalities

  • Dario Cordero-Erausquin
  • Bo’az Klartag
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)

Abstract

We survey some interplays between spectral estimates of Hörmander-type, degenerate Monge-Ampère equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santaló or Busemann inequalities.

Keywords

Unit Ball Convex Body Plurisubharmonic Function Complex Interpolation Reinhardt Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We thank Yanir Rubinstein and Bo Berndtsson for interesting, related discussions. Bo’az Klartag was supported in part by the Israel Science Foundation and by a Marie Curie Reintegration Grant from the Commission of the European Communities.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuUniversité Pierre et Marie Curie (Paris 6)ParisFrance
  2. 2.Institut Universitaire de FranceParisFrance
  3. 3.School of Mathematical Sciences, Sackler Faculty of Exact SciencesTel-Aviv UniversityTel AvivIsrael

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