Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume |
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Authors: | Alessio FIGALLI and David JERISON |
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Institution: | 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 |
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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|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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Keywords: | Quantitative stability Brunn-Minkowski Affine geometry Convex geometry Additive combinatorics |
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