The log-Brunn-Minkowski inequality and the Logarithmic Minkowski Problem

Postgraduate Thesis uoadl:1692003 736 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2017-06-30
Year:
2017
Author:
Kalantzopoulos Pavlos
Supervisors info:
Απόστολος Γιαννόπουλος Καθηγητής Τμημ. Μαθηματικών ΕΚΠΑ Γατζούρας Δημήτριος Καθηγητής Τμημ. Μαθηματικών ΕΚΠΑ, Μερκουράκης Σοφοκλής Καθηγητής Τμήμα Μαθηματικών ΕΚΠΑ
Original Title:
Λογαριθμική ανισότητα Brunn-Minkowski και το λογαριθμικό πρόβλημα Minkowski
Languages:
Greek
Translated title:
The log-Brunn-Minkowski inequality and the Logarithmic Minkowski Problem
Summary:
n this Thesis we study two open problems from the Brunn-Minkowski theory. The main theme is the interplay between vector addition and volume of convex bodies in Euclidean space.
In the first part of the Thesis, we study the question whether the logarithmic Brunn-Minkowski inequality, a stronger inequality than the classical Brunn-Minkowski inequality, holds true for the class of the symmetric convex bodies. We present the known, up to now, results and partial answers to this question.
In the second part of the Thesis, we study the Minkowski problem for the cone-volume measure. The question is to give necessary and sufficient conditions for a Borel measure on the sphere so that it is the cone-volume measure of a convex body. We present the answer to this question in the symmetric case. The crucial condition is related to the concentration of measure on spheres of subspaces of lower dimension.
Main subject category:
Science
Other subject categories:
Mathematics
Keywords:
surface area measure, cone-volume measure, Minkowski Problem, log-Minkowski problem
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
10
Number of pages:
91
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