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| Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume |
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Citation： |
Alessio FIGALLI,David JERISON.Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume[J].Chinese Annals of Mathematics B,2017,38(2):393~412 |
| Page view： 653
Net amount： 687 |
Authors： |
Alessio FIGALLI; David JERISON |
Foundation： |
This work was supported by NSF Grant DMS-1262411, NSF Grant
DMS-1361122, NSF Grant DMS-1069225 and DMS-1500771. |
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| Abstract： |
The authors prove a quantitative stability result for the
Brunn-Minkowski inequality on sets of equal volume: If $|A|=|B|>0$
and $|A+B|^{\frac{1}{n}}=(2+\delta)|A|^{\frac{1}{n}}$ for some small
$\delta$, then, up to a translation, both $A$ and $B$ are close (in
terms of $\delta$) 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. |
Keywords： |
Quantitative stability, Brunn-Minkowski, Affine geometry, Convexgeometry, Additive combinatorics |
Classification： |
49Q20, 52A40, 52A20, 11P70 |
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