On simplexes inscribed in a hypersurface

Mikhael Gromov

Research output: Contribution to journalArticle

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 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
Volume5
Issue number1
DOIs
StatePublished - Jan 1969

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Hypersurface
Homeomorphic
Convex Hull
Sufficient Conditions
Form

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On simplexes inscribed in a hypersurface. / Gromov, Mikhael.

In: Mathematical Notes of the Academy of Sciences of the USSR, Vol. 5, No. 1, 01.1969, p. 52-56.

Research output: Contribution to journalArticle

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