Lp dual curvature measures

Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.1016/j.aim.2018.02.011

L_p dual curvature measures

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

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

Abstract

A new family of geometric Borel measures on the unit sphere is introduced. Special cases include the L_p surface area measures (which extend the classical surface area measure of Aleksandrov and Fenchel & Jessen) and L_p-integral curvature (which extends Alkesandrov's integral curvature) in the L_p Brunn–Minkowski theory. It also includes the dual curvature measures (which are the duals of Federer's curvature measures) in the dual Brunn–Minkowski theory. This partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes.

Original language	English (US)
Pages (from-to)	85-132
Number of pages	48
Journal	Advances in Mathematics
Volume	329
DOIs	https://doi.org/10.1016/j.aim.2018.02.011
State	Published - Apr 30 2018

Keywords

Alexandrov problem
Dual Brunn–Minkowski theory
Dual curvature measures
Integral curvature
L Brunn–Minkowski theory
L-Minkowski problem

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.aim.2018.02.011

Cite this

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title = "Lp dual curvature measures",

abstract = "A new family of geometric Borel measures on the unit sphere is introduced. Special cases include the Lp surface area measures (which extend the classical surface area measure of Aleksandrov and Fenchel & Jessen) and Lp-integral curvature (which extends Alkesandrov's integral curvature) in the Lp Brunn–Minkowski theory. It also includes the dual curvature measures (which are the duals of Federer's curvature measures) in the dual Brunn–Minkowski theory. This partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes.",

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AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

PY - 2018/4/30

Y1 - 2018/4/30

N2 - A new family of geometric Borel measures on the unit sphere is introduced. Special cases include the Lp surface area measures (which extend the classical surface area measure of Aleksandrov and Fenchel & Jessen) and Lp-integral curvature (which extends Alkesandrov's integral curvature) in the Lp Brunn–Minkowski theory. It also includes the dual curvature measures (which are the duals of Federer's curvature measures) in the dual Brunn–Minkowski theory. This partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes.

AB - A new family of geometric Borel measures on the unit sphere is introduced. Special cases include the Lp surface area measures (which extend the classical surface area measure of Aleksandrov and Fenchel & Jessen) and Lp-integral curvature (which extends Alkesandrov's integral curvature) in the Lp Brunn–Minkowski theory. It also includes the dual curvature measures (which are the duals of Federer's curvature measures) in the dual Brunn–Minkowski theory. This partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes.

KW - Alexandrov problem

KW - Dual Brunn–Minkowski theory

KW - Dual curvature measures

KW - Integral curvature

KW - L Brunn–Minkowski theory

KW - L-Minkowski problem

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