TY - JOUR
T1 - Boundary restricted Brunn-Minkowski inequalities
AU - Artstein-Avidan, Shiri
AU - Falah, Tomer
AU - Slomka, Boaz A.
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2024/11/1
Y1 - 2024/11/1
N2 - 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.
AB - 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.
KW - Brunn-Minkowski inequality
KW - Minkowski addition
KW - boundary
KW - convex bodies
UR - http://www.scopus.com/inward/record.url?scp=85181688429&partnerID=8YFLogxK
U2 - 10.1142/S0219199723500566
DO - 10.1142/S0219199723500566
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AN - SCOPUS:85181688429
SN - 0219-1997
VL - 26
SP - 1
EP - 14
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
IS - 9
M1 - 2350056
ER -