The LP-Aleksandrov problem for LP-integral curvature

Yong Huang; Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.4310/jdg/1536285625

The L_P-Aleksandrov problem for L_P-integral curvature

Yong Huang, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

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

Abstract

It is shown that within the L_p-Brunn–Minkowski theory that Aleksandrov’s integral curvature has a natural L_p extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the L_p-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.

Original language	English (US)
Pages (from-to)	1-29
Number of pages	29
Journal	Journal of Differential Geometry
Volume	110
Issue number	1
DOIs	https://doi.org/10.4310/jdg/1536285625
State	Published - Sep 2018

Keywords

Aleksandrov problem
And phrases. Curvature measure
Integral curvature
Lp-Aleksandrov problem
Lp-Minkowski problem
Lp-integral curvature
Minkowski problem
Surface area measure

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

Access to Document

10.4310/jdg/1536285625

Cite this

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AU - Yang, Deane

AU - Zhang, Gaoyong

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KW - And phrases. Curvature measure

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KW - Lp-Aleksandrov problem

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KW - Lp-integral curvature

KW - Minkowski problem

KW - Surface area measure

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