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 |
| Published: |
Springer Nature,
2021-10-27T20:28:52Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | © 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. |
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