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Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters

Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters

Closed and non-closed (with planar edges) strictly convex surfaces with continuous curvatures are considered. Upper and lower bounds are obtained for the Gaussian curvature under various restrictions imposed on integral parameters of a surface: the diameter and width of the surface, the volume of th...

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Main Author: Babenko, V.I.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2018
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/145855
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spelling irk-123456789-1458552019-02-02T01:23:08Z Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters Babenko, V.I. Closed and non-closed (with planar edges) strictly convex surfaces with continuous curvatures are considered. Upper and lower bounds are obtained for the Gaussian curvature under various restrictions imposed on integral parameters of a surface: the diameter and width of the surface, the volume of the enclosed body, the maximum area of planar cross-sections of the enclosed body, the radius of a circumscribed or inscribed ball, the height of non-closed surface and the area enclosed by the planar boundary of the surface. Розглядаються як замкненi, так i незамкненi з плоским краєм строго опуклi поверхнi з неперервною кривиною. Одержано оцiнки зверху та знизу для гаусової кривини в залежностi вiд заданих обмежень на деякi iнтегральнi параметри поверхнi, такi як: дiаметр або ширина поверхнi, об’єм тiла, яке обмежує поверхня, максимальна площа “поперечного” перерiзу тiла, радiус описаного чи вписаного шару, висота незамкненої поверхнi та площа областi, яку обмежує плоский край поверхнi. 2018 Article Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters / V.I. Babenko // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 3-15. — Бібліогр.: 6 назв. — англ. 1812-9471 DOI: https://doi.org/10.15407/mag14.01.003 Mathematics Subject Classification 2010: 53A05 http://dspace.nbuv.gov.ua/handle/123456789/145855 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description Closed and non-closed (with planar edges) strictly convex surfaces with continuous curvatures are considered. Upper and lower bounds are obtained for the Gaussian curvature under various restrictions imposed on integral parameters of a surface: the diameter and width of the surface, the volume of the enclosed body, the maximum area of planar cross-sections of the enclosed body, the radius of a circumscribed or inscribed ball, the height of non-closed surface and the area enclosed by the planar boundary of the surface.
format Article
author Babenko, V.I.
spellingShingle Babenko, V.I.
Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
Журнал математической физики, анализа, геометрии
author_facet Babenko, V.I.
author_sort Babenko, V.I.
title Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
title_short Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
title_full Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
title_fullStr Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
title_full_unstemmed Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
title_sort estimates for the gaussian curvature of a strictly convex surface and its integral parameters
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2018
url http://dspace.nbuv.gov.ua/handle/123456789/145855
citation_txt Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters / V.I. Babenko // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 3-15. — Бібліогр.: 6 назв. — англ.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT babenkovi estimatesforthegaussiancurvatureofastrictlyconvexsurfaceanditsintegralparameters
first_indexed 2023-05-20T17:23:15Z
last_indexed 2023-05-20T17:23:15Z
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