Abstract

Consider a non-degenerate open convex cone C with vertex the origin in the <TEX>$n$</TEX>2-dimensional Euclidean space <TEX>$E^n$</TEX>. 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 <TEX>$p$</TEX> is independent of the point <TEX>$p{\in}M$</TEX>, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

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