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

Yu Kitabeppu, and Sajjad Lakzian. "Characterization of Low Dimensional RCD*(K, N) Spaces." Analysis and Geometry in Metric Spaces 4.1 (2016): 187-215, electronic only. <http://eudml.org/doc/286750>.

@article{YuKitabeppu2016,
abstract = {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.},
author = {Yu Kitabeppu, Sajjad Lakzian},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Low dimensional; metric measure spaces; Riemannian Ricci curvature bound; curvaturedimension; Bishop-Gromov; Ahlfors regular; Ricci limit spaces; low-dimensional; curvature dimension},
language = {eng},
number = {1},
pages = {187-215, electronic only},
title = {Characterization of Low Dimensional RCD*(K, N) Spaces},
url = {http://eudml.org/doc/286750},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Yu Kitabeppu
AU - Sajjad Lakzian
TI - Characterization of Low Dimensional RCD*(K, N) Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 187
EP - 215, electronic only
AB - 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.
LA - eng
KW - Low dimensional; metric measure spaces; Riemannian Ricci curvature bound; curvaturedimension; Bishop-Gromov; Ahlfors regular; Ricci limit spaces; low-dimensional; curvature dimension
UR - http://eudml.org/doc/286750
ER -