Work

The Loewner function of a log-concave function

Year: 2019

Type: preprint

Abstract: We introduce the notion of Loewner (ellipsoid) function for a log concave function and show that it is an extension of the Loewner ellipsoid for convex bodies. We investigate its duality relation to the recently defined John (ellipsoid) function by Alonso-Gutierrez, Merino, Jimenez and Villa. For convex bodies, John and Loewner ellipsoids are dual to each other. Interestingly, this need not be the case for the John function and the Loewner function.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1904.01211

Authors: Li, Ben, Schuett, Carsten, Werner, Elisabeth M.

Institutions: Tel Aviv University, Christian-Albrechts-Universität zu Kiel, Université de Lille, Université Lille 1, Case Western Reserve University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2926688102

Cites: 37

Cited by: 3

Related to: 10