JOURNAL ARTICLE

Sumset Estimates in Convex Geometry.

  • Published In: IMRN: International Mathematics Research Notices, 2024, v. 2024, n. 15. P. 11426 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Fradelizi, Matthieu; Madiman, Mokshay; Zvavitch, Artem 3 of 3

Abstract

The article investigates continuous analogues of sumset estimates from additive combinatorics in the setting of convex geometry, focusing on volumes of Minkowski sums of convex bodies in Euclidean space \(\mathbb{R}^n\). It establishes that volume is supermodular of arbitrary order on convex bodies and explores sharp constants in convex geometry versions of Plünnecke-Ruzsa inequalities, improving known bounds on constants relating volumes of Minkowski sums. The work also connects these inequalities to classical results such as the Rogers-Shephard inequality and studies extensions involving differences of convex bodies, including a sharp sum-difference inequality in the plane. Additionally, it highlights that many of these inequalities fail without convexity assumptions and provides new results for special classes of convex bodies like ellipsoids and zonoids.

Additional Information

  • Source:IMRN: International Mathematics Research Notices. 2024/08, Vol. 2024, Issue 15, p11426
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:1073-7928
  • DOI:10.1093/imrn/rnae095
  • Accession Number:178887540
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