Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

查看全文 作　　者：Alessio [1]FIGALLI;David [2]JERISON

机构地区：[1]The University of Texas at Austin,Mathematics Dept.RLM 8.100,2515 Speedway Stop C1200,Austin,TX 78712-1202,USA.;[2]Department of Mathematics,Massachusetts Institute of Technology,77 Massachusetts Ave,Cambridge,MA 02139-4307 USA.

出　　处：《Chinese Annals of Mathematics,Series B》索引2017年第38卷第2期,共20页

基　　金：supported by NSF Grant DMS-1262411,NSF Grant DMS-1361122,NSF Grant DMS-1069225 and DMS-1500771 摘　　要：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. 关键词：QUANTITATIVE stability, Brunn-Minkowski, AFFINE geometry, Convexgeometry, Additive COMBINATORICS

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Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

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