On simplexes inscribed in a hypersurface

M. L. Gromov

Research output: Contribution to journalArticlepeer-review


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 Δ ⊂ Rn. In particular, it is shown that if M is a smooth hypersurface, homeomorphic to a sphere, such points will exist for any simplex Δ ⊂ Rn. The proofs are based on simple topological considerations. There are six references.

Original languageEnglish (US)
Pages (from-to)52-56
Number of pages5
JournalMathematical Notes of the Academy of Sciences of the USSR
Issue number1
StatePublished - Jan 1969

ASJC Scopus subject areas

  • General Mathematics


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