Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Chatziantoni Panagiota
Supervisors info:
Γιαννόπουλος Απόστολος, καθηγητής, τμήμα Μαθηματικών, ΕΚΠΑ
Γατζούρας Δημήτριος, καθηγητής, τμήμα Μαθηματικών, ΕΚΠΑ
Χατζηαφράτης Τηλέμαχος, καθηγητής, τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Ανισότητες αναδιάταξης και εφαρμογές στην κυρτή γεωμετρική ανάλυση
Translated title:
Rearrangement inequalities and applications to convex geometric analysis
Summary:
This thesis is devoted to the Brascamp-Lieb-Luttinger inequality and the Brascamp-Lieb inequality, two very strong rearrangement inequalities.
First, we introduce the notion of the symmetric rearrangement of a function and we prove the Brascamp-Lieb-Luttinger inequality as well as its generalization to functions of several variables. In the next chapter we present various applications of these inequalities to stochastic geometry and geometric functional analysis.
Next, we prove the Brascamp-Lieb inequality and its reverse which is due to Barthe. We present the original proof of Brascamp and Lieb as well as Barthe’s proof. We also present the geometric form of these inequalities, which is due to Ball. Finally, we study various applications of the one-dimensional, the reverse and the multi-dimensional geometric Brascamp-Lieb inequality to convex geometry.
Main subject category:
Science
Keywords:
Rearrangement inequalities, Brascamb-Lieb-Luttinger, Brascamb-Lieb, convex geometric analysis
