Journal article

### Measure rigidity of Ricci curvature lower bounds

Abstract:

The measure contraction property, for short, is a weak Ricci curvature lower bound conditions for metric measure spaces. The goal of this paper is to understand which structural properties such assumption (or even weaker modifications) implies on the measure, on its support and on the geodesics of the space. We start our investigation from the Euclidean case by proving that if a positive Radon measure over is such that verifies a weaker variant of , then its support must be convex and h...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Accepted manuscript, pdf, 470.9KB)
Publisher copy:
10.1016/j.aim.2015.09.016

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Elsevier Publisher's website
Journal:
Volume:
286
Issue:
January 2016
Pages:
430-480
Publication date:
2015-10-08
Acceptance date:
2015-09-10
DOI:
EISSN:
1090-2082
ISSN:
0001-8708
Source identifiers:
1061599
Language:
English
Keywords:
Pubs id:
pubs:1061599
UUID:
uuid:9d2576ec-579e-4886-9ff2-9ef37bd806c7
Local pid:
pubs:1061599
Deposit date:
2019-10-18