The Löwner Function of a Log-Concave Function
| Autor: | Ben Li, Carsten Schuett, Elisabeth M. Werner |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Concave function
010102 general mathematics Regular polygon Extension (predicate logic) Function (mathematics) 01 natural sciences Ellipsoid Duality relation Combinatorics John ellipsoid Differential geometry 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | The Journal of Geometric Analysis. 31:423-456 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-019-00270-8 |
| Popis: | We introduce the notion of Lowner (ellipsoid) function for a log-concave function and show that it is an extension of the Lowner ellipsoid for convex bodies. We investigate its duality relation to the recently defined John (ellipsoid) function (Alonso-Gutierrez et al. in J Geom Anal 28:1182–1201, 2018). For convex bodies, John and Lowner ellipsoids are dual to each other. Interestingly, this need not be the case for the John function and the Lowner function. |
| Databáze: | OpenAIRE |
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