"Irrational" constructions in convex geometry

V. Milman; L. Rotem

doi:10.1090/spmj/1487

"Irrational" constructions in convex geometry

V. Milman, L. Rotem

School of Mathematics

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

Abstract

Several ways to define various "irrational" functions of convex bodies, like the geometric mean or power functions, are discussed.

Original language	English (US)
Pages (from-to)	165-175
Number of pages	11
Journal	St. Petersburg Mathematical Journal
Volume	29
Issue number	1
DOIs	https://doi.org/10.1090/spmj/1487
State	Published - 2018

Bibliographical note

Funding Information:
2010 Mathematics Subject Classification. Primary 52A20. Key words and phrases. Convex body, Minkowski sum, support function, ellipsoid, polar body, larity map. Research supported in part by ISF grant 826/13 and BSF grant 2012111.

Publisher Copyright:
© 2017 American Mathematical Society.

Keywords

Convex body
Ellipsoid
Minkowski sum
Polar body
Polarity map
Support function

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10.1090/spmj/1487

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title = "{"}Irrational{"} constructions in convex geometry",

abstract = "Several ways to define various {"}irrational{"} functions of convex bodies, like the geometric mean or power functions, are discussed.",

keywords = "Convex body, Ellipsoid, Minkowski sum, Polar body, Polarity map, Support function",

author = "V. Milman and L. Rotem",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 52A20. Key words and phrases. Convex body, Minkowski sum, support function, ellipsoid, polar body, larity map. Research supported in part by ISF grant 826/13 and BSF grant 2012111. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2018",

doi = "10.1090/spmj/1487",

language = "English (US)",

volume = "29",

pages = "165--175",

journal = "St. Petersburg Mathematical Journal",

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AU - Rotem, L.

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 52A20. Key words and phrases. Convex body, Minkowski sum, support function, ellipsoid, polar body, larity map. Research supported in part by ISF grant 826/13 and BSF grant 2012111. Publisher Copyright: © 2017 American Mathematical Society.

PY - 2018

Y1 - 2018

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AB - Several ways to define various "irrational" functions of convex bodies, like the geometric mean or power functions, are discussed.

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KW - Ellipsoid

KW - Minkowski sum

KW - Polar body

KW - Polarity map

KW - Support function

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"Irrational" constructions in convex geometry

Abstract

Bibliographical note

Keywords

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