Identifying set inclusion by projective positions and mixed volumes

Dan Florentin; Vitali Milman; Alexander Segal

doi:https://doi.org/10.1007/978-3-319-09477-9_11

Identifying set inclusion by projective positions and mixed volumes

Dan Florentin, Vitali Milman, Alexander Segal

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We study a few approaches to identify inclusion (up to a shift) between two convex bodies in Rⁿ. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or surface area of all projective positions of the sets. We prove similar results for Minkowski sums of the sets.

Original language	English
Pages (from-to)	133-145
Number of pages	13
Journal	Lecture Notes in Mathematics
Volume	2116
DOIs	https://doi.org/10.1007/978-3-319-09477-9_11
State	Published - 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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title = "Identifying set inclusion by projective positions and mixed volumes",

abstract = "We study a few approaches to identify inclusion (up to a shift) between two convex bodies in Rn. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or surface area of all projective positions of the sets. We prove similar results for Minkowski sums of the sets.",

author = "Dan Florentin and Vitali Milman and Alexander Segal",

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AU - Florentin, Dan

AU - Milman, Vitali

AU - Segal, Alexander

PY - 2014

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AB - We study a few approaches to identify inclusion (up to a shift) between two convex bodies in Rn. To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or surface area of all projective positions of the sets. We prove similar results for Minkowski sums of the sets.

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U2 - https://doi.org/10.1007/978-3-319-09477-9_11

DO - https://doi.org/10.1007/978-3-319-09477-9_11

M3 - مقالة

SN - 0075-8434

VL - 2116

SP - 133

EP - 145

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

ER -

Identifying set inclusion by projective positions and mixed volumes

Abstract

All Science Journal Classification (ASJC) codes

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