On Lp-Affine Surface Area and Curvature Measures

Yiming Zhao

doi:10.1093/imrn/rnv178

On L_p-Affine Surface Area and Curvature Measures

Yiming Zhao

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

14 Scopus citations

Abstract

The relationship between L_p-affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of L_p-affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Schütt and Werner's.

Original language	English (US)
Pages (from-to)	1387-1423
Number of pages	37
Journal	International Mathematics Research Notices
Volume	2016
Issue number	5
DOIs	https://doi.org/10.1093/imrn/rnv178
State	Published - Jun 19 2016
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1093/imrn/rnv178

Cite this

@article{5202e96eee1e4525b786eb05ef88727e,

title = "On Lp-Affine Surface Area and Curvature Measures",

abstract = "The relationship between Lp-affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of Lp-affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, {"}polar{"} to that of Lutwak's and {"}dual{"} to that of Sch{\"u}tt and Werner's.",

author = "Yiming Zhao",

year = "2016",

month = jun,

day = "19",

doi = "10.1093/imrn/rnv178",

language = "English (US)",

volume = "2016",

pages = "1387--1423",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "5",

}

TY - JOUR

T1 - On Lp-Affine Surface Area and Curvature Measures

AU - Zhao, Yiming

PY - 2016/6/19

Y1 - 2016/6/19

N2 - The relationship between Lp-affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of Lp-affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Schütt and Werner's.

AB - The relationship between Lp-affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of Lp-affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Schütt and Werner's.

UR - http://www.scopus.com/inward/record.url?scp=84973375239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84973375239&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnv178

DO - 10.1093/imrn/rnv178

M3 - Article

AN - SCOPUS:84973375239

SN - 1073-7928

VL - 2016

SP - 1387

EP - 1423

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 5

ER -

On L_p-Affine Surface Area and Curvature Measures

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this