The dual Minkowski problem for symmetric convex bodies
1
3
NYU Tandon School of Engineering
Publication type: Journal Article
Publication date: 2019-11-01
scimago Q1
wos Q1
SJR: 2.094
CiteScore: 3.0
Impact factor: 1.5
ISSN: 00018708, 10902082
General Mathematics
Abstract
The dual Minkowski problem for even data asks what are the necessary and sufficient conditions on a prescribed even measure on the unit sphere for it to be the q-th dual curvature measure of an origin-symmetric convex body in R n . A full solution to this is given when 1 q n . The necessary and sufficient conditions turn out to be an explicit measure concentration condition. To obtain the results, a variational approach is used, where the functional is the sum of a dual quermassintegral and an entropy integral. The proof requires two crucial estimates. The first is an estimate of the entropy integral which is obtained by using a spherical partition. The second is a sharp estimate of the dual quermassintegrals for a carefully chosen barrier convex body.
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Total citations:
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Citations from 2024:
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GOST
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Böröczky K. J. et al. The dual Minkowski problem for symmetric convex bodies // Advances in Mathematics. 2019. Vol. 356. p. 106805.
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Böröczky K. J., Lutwak E., Yang D., Zhang G., Zhao Yiming 赵. The dual Minkowski problem for symmetric convex bodies // Advances in Mathematics. 2019. Vol. 356. p. 106805.
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RIS
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TY - JOUR
DO - 10.1016/j.aim.2019.106805
UR - https://doi.org/10.1016/j.aim.2019.106805
TI - The dual Minkowski problem for symmetric convex bodies
T2 - Advances in Mathematics
AU - Böröczky, Károly J.
AU - Lutwak, Erwin
AU - Yang, Deane
AU - Zhang, Gaoyong
AU - Zhao Yiming, 赵一鸣
PY - 2019
DA - 2019/11/01
PB - Elsevier
SP - 106805
VL - 356
SN - 0001-8708
SN - 1090-2082
ER -
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@article{2019_Böröczky,
author = {Károly J. Böröczky and Erwin Lutwak and Deane Yang and Gaoyong Zhang and 赵一鸣 Zhao Yiming},
title = {The dual Minkowski problem for symmetric convex bodies},
journal = {Advances in Mathematics},
year = {2019},
volume = {356},
publisher = {Elsevier},
month = {nov},
url = {https://doi.org/10.1016/j.aim.2019.106805},
pages = {106805},
doi = {10.1016/j.aim.2019.106805}
}