TY - JOUR
T1 - Some New Positions of Maximal Volume of Convex Bodies
AU - Artstein-Avidan, Shiri
AU - Putterman, Eli
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
PY - 2022/12
Y1 - 2022/12
N2 - In this paper, we extend and generalize several previous works on maximal volume positions of convex bodies. First, we analyze the maximal positive-definite image of one convex body inside another, and the resulting decomposition of the identity. We discuss continuity and differentiability of the mapping associating a body with its positive John position. We then introduce the saddle-John position of one body inside another, proving that it shares some of the properties possessed by the position of maximal volume, and explain how this can be used to improve volume ratio estimates. We investigate several examples in detail and compare these positions. Finally, we discuss the maximal intersection position of one body with respect to another, and show the existence of a natural decomposition of identity associated to this position, extending previous work which treated the case when one of the bodies is the Euclidean ball.
AB - In this paper, we extend and generalize several previous works on maximal volume positions of convex bodies. First, we analyze the maximal positive-definite image of one convex body inside another, and the resulting decomposition of the identity. We discuss continuity and differentiability of the mapping associating a body with its positive John position. We then introduce the saddle-John position of one body inside another, proving that it shares some of the properties possessed by the position of maximal volume, and explain how this can be used to improve volume ratio estimates. We investigate several examples in detail and compare these positions. Finally, we discuss the maximal intersection position of one body with respect to another, and show the existence of a natural decomposition of identity associated to this position, extending previous work which treated the case when one of the bodies is the Euclidean ball.
KW - 52A23
KW - 52A40
KW - Maximal intersection position
KW - Positive John position
UR - http://www.scopus.com/inward/record.url?scp=85195610822&partnerID=8YFLogxK
U2 - 10.1007/s44007-022-00031-0
DO - 10.1007/s44007-022-00031-0
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AN - SCOPUS:85195610822
SN - 2730-9657
VL - 1
SP - 765
EP - 808
JO - Matematica
JF - Matematica
IS - 4
ER -