On L-p-affine surface areas

Elisabeth Werner

doi:10.1512/iumj.2007.56.3099

On L-_p-affine surface areas

Elisabeth Werner

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

56 Scopus citations

Abstract

Let K be a convex body in ℝⁿwith centroid at 0 and B be the Euclidean unit ball in ℝⁿcentered at 0. We show that lim_t→0|K|-|K_t|/|B| _|B_t| =O_p(K)/O_p(B) where |K| respectively |B| denotes the volume of K respectively B, O_p(K) respectively O_p(B) is the p-affine surface area of K respectively B and {K_t}t≥0. {B_t)t≥0 are general families of convex bodies constructed from K, B satisfying certain conditions. As a corollary we get results obtained in [23,25,26,31]. Indiana University Mathematics Journal

Original language	English (US)
Pages (from-to)	2305-2323
Number of pages	19
Journal	Indiana University Mathematics Journal
Volume	56
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2007.56.3099
State	Published - 2007
Externally published	Yes

Keywords

Affine surface area

Publisher link

10.1512/iumj.2007.56.3099

Find It

Find It at U of M Libraries

Cite this

@article{91d27848d35a4fde9c5c3098432fd1fe,

title = "On L-p-affine surface areas",

abstract = "Let K be a convex body in ℝnwith centroid at 0 and B be the Euclidean unit ball in ℝncentered at 0. We show that limt→0|K|-|Kt|/|B| _|Bt| =Op(K)/Op(B) where |K| respectively |B| denotes the volume of K respectively B, Op(K) respectively Op(B) is the p-affine surface area of K respectively B and {Kt}t≥0. {Bt)t≥0 are general families of convex bodies constructed from K, B satisfying certain conditions. As a corollary we get results obtained in [23,25,26,31]. Indiana University Mathematics Journal",

keywords = "Affine surface area",

author = "Elisabeth Werner",

year = "2007",

doi = "10.1512/iumj.2007.56.3099",

language = "English (US)",

volume = "56",

pages = "2305--2323",

journal = "Indiana University Mathematics Journal",

issn = "0022-2518",

publisher = "Indiana University",

number = "5",

}

TY - JOUR

T1 - On L-p-affine surface areas

AU - Werner, Elisabeth

PY - 2007

Y1 - 2007

N2 - Let K be a convex body in ℝnwith centroid at 0 and B be the Euclidean unit ball in ℝncentered at 0. We show that limt→0|K|-|Kt|/|B| _|Bt| =Op(K)/Op(B) where |K| respectively |B| denotes the volume of K respectively B, Op(K) respectively Op(B) is the p-affine surface area of K respectively B and {Kt}t≥0. {Bt)t≥0 are general families of convex bodies constructed from K, B satisfying certain conditions. As a corollary we get results obtained in [23,25,26,31]. Indiana University Mathematics Journal

AB - Let K be a convex body in ℝnwith centroid at 0 and B be the Euclidean unit ball in ℝncentered at 0. We show that limt→0|K|-|Kt|/|B| _|Bt| =Op(K)/Op(B) where |K| respectively |B| denotes the volume of K respectively B, Op(K) respectively Op(B) is the p-affine surface area of K respectively B and {Kt}t≥0. {Bt)t≥0 are general families of convex bodies constructed from K, B satisfying certain conditions. As a corollary we get results obtained in [23,25,26,31]. Indiana University Mathematics Journal

KW - Affine surface area

UR - http://www.scopus.com/inward/record.url?scp=39049124020&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39049124020&partnerID=8YFLogxK

U2 - 10.1512/iumj.2007.56.3099

DO - 10.1512/iumj.2007.56.3099

M3 - Article

AN - SCOPUS:39049124020

SN - 0022-2518

VL - 56

SP - 2305

EP - 2323

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 5

ER -