Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume
© 2017, Fudan University and Springer-Verlag Berlin Heidelberg. The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume: If |A| = |B| > 0 and |A + B|1/n = (2+δ)|A|1/n for some small δ, then, up to a translation, both A and B are close (in terms...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Nature
2021
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| Online Access: | https://hdl.handle.net/1721.1/135700 |
| _version_ | 1826194153363472384 |
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| author | Figalli, Alessio Jerison, David |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Figalli, Alessio Jerison, David |
| author_sort | Figalli, Alessio |
| collection | MIT |
| description | © 2017, Fudan University and Springer-Verlag Berlin Heidelberg. The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume: If |A| = |B| > 0 and |A + B|1/n = (2+δ)|A|1/n for some small δ, then, up to a translation, both A and B are close (in terms of δ) to a convex set K. Although this result was already proved by the authors in a previous paper, the present paper provides a more elementary proof that the authors believe has its own interest. Also, the result here provides a stronger estimate for the stability exponent than the previous result of the authors. |
| first_indexed | 2024-09-23T09:51:45Z |
| format | Article |
| id | mit-1721.1/135700 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:51:45Z |
| publishDate | 2021 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | mit-1721.1/1357002023-02-24T21:42:12Z Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume Figalli, Alessio Jerison, David Massachusetts Institute of Technology. Department of Mathematics © 2017, Fudan University and Springer-Verlag Berlin Heidelberg. The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume: If |A| = |B| > 0 and |A + B|1/n = (2+δ)|A|1/n for some small δ, then, up to a translation, both A and B are close (in terms of δ) to a convex set K. Although this result was already proved by the authors in a previous paper, the present paper provides a more elementary proof that the authors believe has its own interest. Also, the result here provides a stronger estimate for the stability exponent than the previous result of the authors. 2021-10-27T20:28:52Z 2021-10-27T20:28:52Z 2017 2021-04-29T14:29:02Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135700 Figalli, Alessio, and David Jerison. "Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume." Chinese Annals of Mathematics Series B 38 2 (2017): 393-412. en 10.1007/S11401-017-1075-8 Chinese Annals of Mathematics. Series B Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Nature Other repository |
| spellingShingle | Figalli, Alessio Jerison, David Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume |
| title | Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume |
| title_full | Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume |
| title_fullStr | Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume |
| title_full_unstemmed | Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume |
| title_short | Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume |
| title_sort | quantitative stability of the brunn minkowski inequality for sets of equal volume |
| url | https://hdl.handle.net/1721.1/135700 |
| work_keys_str_mv | AT figallialessio quantitativestabilityofthebrunnminkowskiinequalityforsetsofequalvolume AT jerisondavid quantitativestabilityofthebrunnminkowskiinequalityforsetsofequalvolume |