# A rough curvature-dimension condition for metric measure spaces

Open Mathematics (2014)

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

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topAnca-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 -

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