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

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 187-215, electronic only
- ISSN: 2299-3274

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topYu 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 -

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