Limit cone

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)

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