A CHARACTERIZATION OF ELLIPTIC HYPERBOLOIDS

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 1,  2013, pp.37-49
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.1.37
Title & Authors
A CHARACTERIZATION OF ELLIPTIC HYPERBOLOIDS
Kim, Dong-Soo; Son, Booseon;

Abstract
Consider a non-degenerate open convex cone C with vertex the origin in the $\small{n}$2-dimensional Euclidean space $\small{E^n}$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $\small{p}$ is independent of the point $\small{p{\in}M}$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.
Keywords
strictly convex hypersurface;elliptic hyperboloid;homogeneous extension;n-dimensional volume;elliptic cone;support function;
Language
English
Cited by
1.
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1.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473
2.
Revisiting floating bodies, Expositiones Mathematicae, 2016, 34, 4, 396
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Areas associated with a Strictly Locally Convex Curve, Kyungpook mathematical journal, 2016, 56, 2, 583
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