A rough curvature-dimension condition for metric measure spaces

Anca-Iuliana Bonciocat

Open Mathematics (2014)

  • Volume: 12, Issue: 2, page 362-380
  • ISSN: 2391-5455

Abstract

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We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.

How to cite

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Anca-Iuliana Bonciocat. "A rough curvature-dimension condition for metric measure spaces." Open Mathematics 12.2 (2014): 362-380. <http://eudml.org/doc/269637>.

@article{Anca2014,
abstract = {We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.},
author = {Anca-Iuliana Bonciocat},
journal = {Open Mathematics},
keywords = {Optimal transport; Entropy; Wasserstein metric; Curvature-dimension condition; Discrete spaces; metric measure spaces; curvature-dimension condition; rough geodesic; optimal transport; discrete spaces},
language = {eng},
number = {2},
pages = {362-380},
title = {A rough curvature-dimension condition for metric measure spaces},
url = {http://eudml.org/doc/269637},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Anca-Iuliana Bonciocat
TI - A rough curvature-dimension condition for metric measure spaces
JO - Open Mathematics
PY - 2014
VL - 12
IS - 2
SP - 362
EP - 380
AB - We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as well. For spaces that satisfy a rough curvature-dimension condition we prove a generalized Brunn-Minkowski inequality and a Bonnet-Myers type theorem.
LA - eng
KW - Optimal transport; Entropy; Wasserstein metric; Curvature-dimension condition; Discrete spaces; metric measure spaces; curvature-dimension condition; rough geodesic; optimal transport; discrete spaces
UR - http://eudml.org/doc/269637
ER -

References

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