Characterization of Low Dimensional RCD*(K, N) Spaces

• Autorzy: Yu Kitabeppu , Sajjad Lakzian
• Języki publikacji: EN

Abstrakty

EN

In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking, a converse to the Lévy-Gromov’s isoperimetric inequality and was previously only known for Ricci limit spaces) which might be also of independent interest.

Słowa kluczowe

EN

Low dimensional; metric measure spaces; Riemannian Ricci curvature bound; curvaturedimension; Bishop-Gromov; Ahlfors regular; Ricci limit spaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-05-12

zaakceptowano

2016-07-21

online

2016-09-20

Twórcy

autor

Yu Kitabeppu

• Kyoto University

autor

Sajjad Lakzian

• Mathematics Department, Fordham University

Identyfikatory

DOI

10.1515/agms-2016-0007