S. Elsamani. CENTRAL ASIAN JOURNAL OF THEORETICAL AND APPLIED SCIENCE, 4 (5):
147-162(May 2023)
Abstract
Origin-centered balls only, when , and only for balls when is the curvature of a smooth, strictly convex body in in known to be constant. Only for origin-symmetric ellipsoids does the --curvature remain constant if . Using the global stability result from 5, we demonstrate that for 0, the volume symmetric difference between K and a translation of the unit ball B is nearly zero if the -curvature is approximately constant. Here, we have K shrunk to the same volume of a unit ball, denoted by K. We demonstrate a comparable result for in the -distance class of origin-symmetric entities. We also demonstrate a local stability conclusion for : Any strictly convex body with 'nearly' constant curvature is 'almost' the unit ball, and this neighborhood surrounds the unit ball. Both a global stability result in R2 for and a local stability result for in the Banach-Mazur distance are demonstrated.
%0 Journal Article
%1 noauthororeditor
%A Elsamani, Salih Yousuf Mohamed Salih | Shahinaz.A.
%D 2023
%J CENTRAL ASIAN JOURNAL OF THEORETICAL AND APPLIED SCIENCE
%K Minkowski curvature function, inequality
%N 5
%P 147-162
%T Local and Global Stability of the - Curvature
%U https://cajotas.centralasianstudies.org/index.php/CAJOTAS/article/view/1176/1227
%V 4
%X Origin-centered balls only, when , and only for balls when is the curvature of a smooth, strictly convex body in in known to be constant. Only for origin-symmetric ellipsoids does the --curvature remain constant if . Using the global stability result from 5, we demonstrate that for 0, the volume symmetric difference between K and a translation of the unit ball B is nearly zero if the -curvature is approximately constant. Here, we have K shrunk to the same volume of a unit ball, denoted by K. We demonstrate a comparable result for in the -distance class of origin-symmetric entities. We also demonstrate a local stability conclusion for : Any strictly convex body with 'nearly' constant curvature is 'almost' the unit ball, and this neighborhood surrounds the unit ball. Both a global stability result in R2 for and a local stability result for in the Banach-Mazur distance are demonstrated.
@article{noauthororeditor,
abstract = {Origin-centered balls only, when , and only for balls when is the curvature of a smooth, strictly convex body in in known to be constant. Only for origin-symmetric ellipsoids does the --curvature remain constant if . Using the global stability result from [5], we demonstrate that for 0, the volume symmetric difference between K and a translation of the unit ball B is nearly zero if the -curvature is approximately constant. Here, we have K shrunk to the same volume of a unit ball, denoted by K. We demonstrate a comparable result for in the -distance class of origin-symmetric entities. We also demonstrate a local stability conclusion for : Any strictly convex body with 'nearly' constant curvature is 'almost' the unit ball, and this neighborhood surrounds the unit ball. Both a global stability result in R2 for and a local stability result for in the Banach-Mazur distance are demonstrated. },
added-at = {2023-09-23T09:07:56.000+0200},
author = {Elsamani, Salih Yousuf Mohamed Salih | Shahinaz.A.},
biburl = {https://www.bibsonomy.org/bibtex/264618b029fb53e870e0dc5ca24e59afc/centralasian_20},
interhash = {fceb4461a16c0df4613d57161f860d4a},
intrahash = {64618b029fb53e870e0dc5ca24e59afc},
issn = {2660-5317},
journal = {CENTRAL ASIAN JOURNAL OF THEORETICAL AND APPLIED SCIENCE},
keywords = {Minkowski curvature function, inequality},
language = {english},
month = may,
number = 5,
pages = {147-162},
timestamp = {2023-09-23T09:07:56.000+0200},
title = {Local and Global Stability of the - Curvature},
url = {https://cajotas.centralasianstudies.org/index.php/CAJOTAS/article/view/1176/1227},
volume = 4,
year = 2023
}