On simplexes inscribed in a hypersurface |
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Authors: | M. L. Gromov |
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Affiliation: | (1) Leningrad Zhdanov State University, USSR |
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Abstract: | The sufficient conditions are obtained for the existence, on a hyper surface M Rn, of k points whose convex hull forms a (k–1)-dimensional simplex, homothetic to a given simplex Rn. In particular, it is shown that if M is a smooth hypersurface, homeomorphic to a sphere, such points will exist for any simplex Rn. The proofs are based on simple topological considerations. There are six references.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 81–89, January, 1969. |
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