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.
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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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Cordero-Erausquin, D., Klartag, B. (2012). Interpolations, Convexity and Geometric Inequalities. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_9
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DOI: https://doi.org/10.1007/978-3-642-29849-3_9
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