OPTIMAL MAPS AND LOCAL-TO-GLOBAL PROPERTY IN NEGATIVE DIMENSIONAL SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW

Mattia Magnabosco; Chiara Rigoni

doi:10.2748/tmj.20220420

OPTIMAL MAPS AND LOCAL-TO-GLOBAL PROPERTY IN NEGATIVE DIMENSIONAL SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW

Mattia Magnabosco, Chiara Rigoni

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

Original language	English
Pages (from-to)	483-507
Number of pages	25
Journal	Tohoku Mathematical Journal
Volume	75
Issue number	4
DOIs	https://doi.org/10.2748/tmj.20220420
Publication status	Published - 2023

Austrian Fields of Science 2012

101006 Differential geometry
101002 Analysis

Keywords

CD spaces
local-to-global property
negative dimension
Optimal transport maps

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10.2748/tmj.20220420

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title = "OPTIMAL MAPS AND LOCAL-TO-GLOBAL PROPERTY IN NEGATIVE DIMENSIONAL SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW",

abstract = "In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.",

keywords = "CD spaces, local-to-global property, negative dimension, Optimal transport maps",

author = "Mattia Magnabosco and Chiara Rigoni",

note = "Funding Information: 2010 Mathematics Subject Classification.Primary 30L99; Secondary 49N99. Key words and phrases. Optimal transport maps, local-to-global property, CD spaces, negative dimension. * The second author gratefully acknowledges support by the European Union through the ERC-AdG 694405 RicciBounds. Publisher Copyright: {\textcopyright} 2023 Tohoku University, Mathematical Institute. All rights reserved.",

year = "2023",

doi = "10.2748/tmj.20220420",

language = "English",

volume = "75",

pages = "483--507",

journal = "Tohoku Mathematical Journal",

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AU - Rigoni, Chiara

N1 - Funding Information: 2010 Mathematics Subject Classification.Primary 30L99; Secondary 49N99. Key words and phrases. Optimal transport maps, local-to-global property, CD spaces, negative dimension. * The second author gratefully acknowledges support by the European Union through the ERC-AdG 694405 RicciBounds. Publisher Copyright: © 2023 Tohoku University, Mathematical Institute. All rights reserved.

PY - 2023

Y1 - 2023

N2 - In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

AB - In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

KW - CD spaces

KW - local-to-global property

KW - negative dimension

KW - Optimal transport maps

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DO - 10.2748/tmj.20220420

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JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

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ER -

OPTIMAL MAPS AND LOCAL-TO-GLOBAL PROPERTY IN NEGATIVE DIMENSIONAL SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW

Abstract

Austrian Fields of Science 2012

Keywords

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