Difference between revisions of "Limit cone"
From Encyclopedia of Mathematics
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| − | ''of a convex surface | + | {{TEX|done}} |
| + | ''of a convex surface $S$'' | ||
| − | The surface | + | The surface $P(S)$ of the cone formed by the straight half-lines emanating from some point $O\in S$ and belonging to the convex body bounded by $S$. The limit cone is defined uniquely, up to a parallel displacement depending on the choice of $O$. The notion of a limit cone is also defined for certain classes of non-convex surfaces, e.g. for so-called spherical one-sheet saddle surfaces. |
====References==== | ====References==== | ||
Latest revision as of 05:57, 18 October 2014
of a convex surface $S$
The surface $P(S)$ of the cone formed by the straight half-lines emanating from some point $O\in S$ and belonging to the convex body bounded by $S$. The limit cone is defined uniquely, up to a parallel displacement depending on the choice of $O$. The notion of a limit cone is also defined for certain classes of non-convex surfaces, e.g. for so-called spherical one-sheet saddle surfaces.
References
| [1] | A.V. Pogorelov, "Extrinsic geometry of convex surfaces" , Amer. Math. Soc. (1972) (Translated from Russian) |
Comments
References
| [a1] | R. Schneider, "Boundary structure and curvature of convex bodies" J. Tölke (ed.) J.M. Wills (ed.) , Contributions to geometry , Birkhäuser (1979) pp. 13–59 |
| [a2] | H. Busemann, "Convex surfaces" , Interscience (1958) pp. Chapt. III, Sect. 15 |
How to Cite This Entry:
Limit cone. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Limit_cone&oldid=33769
Limit cone. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Limit_cone&oldid=33769
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article