Unit:
Τομέας Μαθηματικής ΑνάλυσηςLibrary of the School of Science
Author:
Σταυρακάκης Παντελής
Dissertation committee:
Καθηγητής Απόστολος Γιαννόπουλος (επιβλέπων)
Original Title:
Γεωμετρία των l_q κεντροειδών σωμάτων
Translated title:
Geometry of Lq-centroid bodies
Summary:
The first chapter contains the basic results of the PhD thesis. In the second
chapter we give the basic definitions and the basic theorems of the theory
which we will use to prove our results. In the third chapter we define the log-
concave probability measures and we present the basic theory of this class of
measures which we will use in our results. In the forth chapter we give some
results about the local stucture of the Lq centroid bodies and some
aplications. The first basic result is about the projections of the Lq centroid
bodies. As a consiquence we get an upper bound of the covering numbers of the
eucledian ball of the centroid bodies. Finally we give an upper bound of the
averange norm of a symmetric convex body. In the fifth we give proove an upper
bound of the average of the volume of the section of a symmetric convex body C
and a random rotation of C U(C). We also give an lower bound of the volume of
the section of a symmetric convex bo dy C and the U( C ), where U is a random
rotation. In the end of this cchapter we give more information about the local
structure of the Lq centroid bodies. In the sixth chapter we define the
quantity Yq(K,M) where K,M are two compact convex bodies and we give some upper
bounds of this quantity.
Keywords:
Isotropic, Centroid, Bodies, Random, Rotations
Number of pages:
[5], 124
