Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below
We prove existence and uniqueness of optimal maps on RCD ∗ ( K , N ) spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of RCD ∗ ( K , N ) bounds.
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| Veröffentlicht in: | The Journal of Geometric Analysis 2016-10, Vol.26 (4), p.2914-2929 |
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| container_end_page | 2929 |
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| container_issue | 4 |
| container_start_page | 2914 |
| container_title | The Journal of Geometric Analysis |
| container_volume | 26 |
| creator | Gigli, Nicola Rajala, Tapio Sturm, Karl-Theodor |
| description | We prove existence and uniqueness of optimal maps on
RCD
∗
(
K
,
N
)
spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of
RCD
∗
(
K
,
N
)
bounds. |
| doi_str_mv | 10.1007/s12220-015-9654-y |
| format | Article |
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RCD
∗
(
K
,
N
)
spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of
RCD
∗
(
K
,
N
)
bounds.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-015-9654-y</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Convex and Discrete Geometry ; Curvature ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Mathematics ; Mathematics and Statistics ; Uniqueness</subject><ispartof>The Journal of Geometric Analysis, 2016-10, Vol.26 (4), p.2914-2929</ispartof><rights>Mathematica Josephina, Inc. 2015</rights><rights>COPYRIGHT 2016 Springer</rights><rights>Copyright Springer Science & Business Media 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-575c1be00469d2393c61832a7d7e4b2315a0eafbcde12d094413d06da1897ea43</citedby><cites>FETCH-LOGICAL-c355t-575c1be00469d2393c61832a7d7e4b2315a0eafbcde12d094413d06da1897ea43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12220-015-9654-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-015-9654-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Gigli, Nicola</creatorcontrib><creatorcontrib>Rajala, Tapio</creatorcontrib><creatorcontrib>Sturm, Karl-Theodor</creatorcontrib><title>Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>We prove existence and uniqueness of optimal maps on
RCD
∗
(
K
,
N
)
spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of
RCD
∗
(
K
,
N
)
bounds.</description><subject>Abstract Harmonic Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Curvature</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Uniqueness</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kE1rHSEUhofSQNOkP6A7oWvTo47jzDK5-WghIZAP6E68eiY13KtTdZLcf18v00U2RUE5vI-8Pk3zlcEJA1DfM-OcAwUm6dDJlu4-NIdMyoEC8F8f6x0k0G7g3afmc87PAG0nWnXYuNup-K3ZkBszZWKCIxdvUwwYijfFx0DqvvTBF6Tnfosh11lN30_GYiavvvwmd95aT1ZzejFlTkjO4hwcOjKmuCVnuImvx83BaDYZv_w7j5rHy4uH1Q96fXv1c3V6Ta2QslCppGVr3HcbHBeDsB3rBTfKKWzXXDBpAM24tg4ZdzC0LRMOOmdYPyg0rThqvi3vTin-mTEX_RznVPtmzfoeetVK1dXUyZJ6MhvUPoyxJGPrcrj1tv599HV-qkAJMUjJK8AWwKaYc8JRT6k6SzvNQO_t68W-rvb13r7eVYYvTK7Z8ITpXZX_Qn8BtWiH6g</recordid><startdate>20161001</startdate><enddate>20161001</enddate><creator>Gigli, Nicola</creator><creator>Rajala, Tapio</creator><creator>Sturm, Karl-Theodor</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope></search><sort><creationdate>20161001</creationdate><title>Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below</title><author>Gigli, Nicola ; Rajala, Tapio ; Sturm, Karl-Theodor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-575c1be00469d2393c61832a7d7e4b2315a0eafbcde12d094413d06da1897ea43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Curvature</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gigli, Nicola</creatorcontrib><creatorcontrib>Rajala, Tapio</creatorcontrib><creatorcontrib>Sturm, Karl-Theodor</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gigli, Nicola</au><au>Rajala, Tapio</au><au>Sturm, Karl-Theodor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2016-10-01</date><risdate>2016</risdate><volume>26</volume><issue>4</issue><spage>2914</spage><epage>2929</epage><pages>2914-2929</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>We prove existence and uniqueness of optimal maps on
RCD
∗
(
K
,
N
)
spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation and to the local-to-global property of
RCD
∗
(
K
,
N
)
bounds.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-015-9654-y</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1050-6926 |
| ispartof | The Journal of Geometric Analysis, 2016-10, Vol.26 (4), p.2914-2929 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_proquest_journals_1880874576 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Curvature Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics Uniqueness |
| title | Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below |
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