Calculus of Variations and Geometric Measure Theory

E. Bruè

Structure of non-smooth spaces with Ricci curvature bounded below

created by bruè on 17 Nov 2020


Ph.D. Thesis

Inserted: 17 nov 2020
Last Updated: 17 nov 2020

Year: 2020


This thesis is devoted to the study of structural properties of non-smooth spaces with Ricci curvature bounded from below. The first part concerns with the structure theory of RCD(K,N) spaces: we prove the existence of the so-called essential dimension, along with rectifiability properties of the regular set. This theory is a result of many contributions 43,72,91,95,109,121, in our presentation we closely follow the recent works 41,43. The second part of this thesis deals with codimension-1 structures on RCD(K,N) spaces. More precisely we study structural properties of boundaries of sets with finite perimeter, generalising the celebrated De Giorgi theory 65, 66 to this framework. This is based on the works 7,40.