Boundary restricted Brunn-Minkowski inequalities

Shiri Artstein-Avidan, Tomer Falah, Boaz A. Slomka

Research output: Contribution to journalArticlepeer-review


In this paper, we explore questions regarding the Minkowski sum of the boundaries of convex sets. Motivated by a question suggested to us by V. Milman regarding the volume of ∂K + ∂T where K and T are convex bodies, we prove sharp volumetric lower bounds for the Minkowski average of the boundaries of sets with connected boundary, as well as some related results.

Original languageEnglish
Article number2350056
JournalCommunications in Contemporary Mathematics
StateAccepted/In press - 2023

Bibliographical note

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© 2023 World Scientific Publishing Company.


  • Brunn-Minkowski inequality
  • Minkowski addition
  • boundary
  • convex bodies


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