The theory of curvature-dimension bounds for nonsmooth spaces has several motivations: the study of functional and geometric inequalities in structures which arc very far from being Euclidean, therefore with new non-Riemannian tools, the description of the “closure” of classes of Riemannian manifolds under suitable geometric constraints, the stability of analytic and geometric properties of spaces (e.g. to prove rigidity results). Even though these goals may occasionally be in conflict, in the last few years we have seen spectacular developments in all these directions, and my text is meant both as a survey and as an introduction to this quickly developing research field.

Calculus, heat flow and curvature-dimension bounds in metric measure spaces

Ambrosio, Luigi
2019

Abstract

The theory of curvature-dimension bounds for nonsmooth spaces has several motivations: the study of functional and geometric inequalities in structures which arc very far from being Euclidean, therefore with new non-Riemannian tools, the description of the “closure” of classes of Riemannian manifolds under suitable geometric constraints, the stability of analytic and geometric properties of spaces (e.g. to prove rigidity results). Even though these goals may occasionally be in conflict, in the last few years we have seen spectacular developments in all these directions, and my text is meant both as a survey and as an introduction to this quickly developing research field.
2019
Settore MAT/05 - Analisi Matematica
International Congress of Mathematicians 2018
Rio de Janeiro, Brazil
1-9 August 2018
Proceedings of the International Congress of Mathematicians 2018
978-981-3272-87-3
File in questo prodotto:
File Dimensione Formato  
ICM_Ambrosio.pdf

accesso aperto

Descrizione: This is a post-peer-review version of a proceedings published in "Proceedings of the International Congress of Mathematicians (ICM 2018)”, pp. 301-340 (2019). The final authenticated version is available online at: https://doi.org/10.1142/9789813272880_0015.
Tipologia: Accepted version (post-print)
Licenza: Creative Commons
Dimensione 1.12 MB
Formato Adobe PDF
1.12 MB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/91035
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? ND
social impact