Neighborly embedded manifolds

G. Kalai*, A. Wigderson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

An embedding of an n-dimensional manifold M into R d is called k-neighborly if, for every k points on the embedded manifold, there is a hyperplane H in R d which supports the manifold precisely at these points. Micha A. Perles (Problems presented in Oberwolfach conference on "Convexity", [1982]) asked: What is the smallest dimension d(k,n) of the ambient space in which a k-neighborly n-dimensional manifold exists? We prove that d(k,n)≤2k(k-1)n. Related results and open problems are discussed.

Original languageEnglish
Pages (from-to)319-324
Number of pages6
JournalDiscrete and Computational Geometry
Volume40
Issue number3
DOIs
StatePublished - Oct 2008

Keywords

  • Continuous hashing
  • Convex bodies
  • Cyclic polytopes
  • Neighborliness
  • Polytopes

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