We attempt to provide a description of the geometric theory of log-concave functions. We present the main aspects of this theory: operations between log-concave functions; duality; inequalities including the Pr´ekopa-Leindler inequality and the functional form of Blaschke-Santal´o inequality and its converse; functional versions of area measure and mixed volumes; valuations on log-concave functions.
Log-concave functions / Colesanti, Andrea. - STAMPA. - (2017), pp. 487-524. [10.1007/978-1-4939-7005-6]
Log-concave functions
A. Colesanti
2017
Abstract
We attempt to provide a description of the geometric theory of log-concave functions. We present the main aspects of this theory: operations between log-concave functions; duality; inequalities including the Pr´ekopa-Leindler inequality and the functional form of Blaschke-Santal´o inequality and its converse; functional versions of area measure and mixed volumes; valuations on log-concave functions.
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