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].

Structure of non-smooth spaces with Ricci curvature bounded below / Bruè, Elia. - (2020 Oct 20).

Structure of non-smooth spaces with Ricci curvature bounded below

BRUÈ, Elia
2020-10-20

Abstract

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].
Settore MAT/05 - Analisi Matematica
Matematica
AMBROSIO, Luigi
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Descrizione: doctoral thesis full text
Tipologia: Tesi PhD
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/90619
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