Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume View Full Text


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Article Info

DATE

2017-03-02

AUTHORS

Alessio Figalli, David Jerison

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. More... »

PAGES

393-412

References to SciGraph publications

  • 2015. Stability results for the Brunn-Minkowski inequality in COLLOQUIUM DE GIORGI 2013 AND 2014
  • 1988-09. On the Brunn-Minkowski theorem in GEOMETRIAE DEDICATA
  • 2010-06-01. A mass transportation approach to quantitative isoperimetric inequalities in INVENTIONES MATHEMATICAE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11401-017-1075-8

    DOI

    http://dx.doi.org/10.1007/s11401-017-1075-8

    DIMENSIONS

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