Absolutely minimal Lipschitz extension of tree-valued mappings
We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics—a generalization of a game called Tug of War that has been used in Peres...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2013
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| Online Access: | http://hdl.handle.net/1721.1/80844 https://orcid.org/0000-0002-5951-4933 |
| _version_ | 1826200029271949312 |
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| author | Naor, Assaf Sheffield, Scott Roger |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Naor, Assaf Sheffield, Scott Roger |
| author_sort | Naor, Assaf |
| collection | MIT |
| description | We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics—a generalization of a game called Tug of War that has been used in Peres et al. (J Am Math Soc 22(1):167–210, 2009) to study real-valued AMLEs. |
| first_indexed | 2024-09-23T11:29:47Z |
| format | Article |
| id | mit-1721.1/80844 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:29:47Z |
| publishDate | 2013 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/808442022-09-27T19:55:46Z Absolutely minimal Lipschitz extension of tree-valued mappings Naor, Assaf Sheffield, Scott Roger Massachusetts Institute of Technology. Department of Mathematics Sheffield, Scott Roger We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics—a generalization of a game called Tug of War that has been used in Peres et al. (J Am Math Soc 22(1):167–210, 2009) to study real-valued AMLEs. National Science Foundation (U.S.) (NSF Grant CCF-0832795) National Science Foundation (U.S.) (NSF Grant CCF-0635078) United States-Israel Binational Science Foundation (BSF grant 2006009) National Science Foundation (U.S.) (NSF Grant OISE-0730136) National Science Foundation (U.S.) (NSF Grant DMS-0645585) 2013-09-20T17:34:04Z 2013-09-20T17:34:04Z 2011-11 2011-10 Article http://purl.org/eprint/type/JournalArticle 0025-5831 1432-1807 http://hdl.handle.net/1721.1/80844 Naor, Assaf, and Scott Sheffield. “Absolutely minimal Lipschitz extension of tree-valued mappings.” Mathematische Annalen 354, no. 3 (November 15, 2012): 1049-1078. https://orcid.org/0000-0002-5951-4933 en_US http://dx.doi.org/10.1007/s00208-011-0753-1 Mathematische Annalen Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Naor, Assaf Sheffield, Scott Roger Absolutely minimal Lipschitz extension of tree-valued mappings |
| title | Absolutely minimal Lipschitz extension of tree-valued mappings |
| title_full | Absolutely minimal Lipschitz extension of tree-valued mappings |
| title_fullStr | Absolutely minimal Lipschitz extension of tree-valued mappings |
| title_full_unstemmed | Absolutely minimal Lipschitz extension of tree-valued mappings |
| title_short | Absolutely minimal Lipschitz extension of tree-valued mappings |
| title_sort | absolutely minimal lipschitz extension of tree valued mappings |
| url | http://hdl.handle.net/1721.1/80844 https://orcid.org/0000-0002-5951-4933 |
| work_keys_str_mv | AT naorassaf absolutelyminimallipschitzextensionoftreevaluedmappings AT sheffieldscottroger absolutelyminimallipschitzextensionoftreevaluedmappings |