A Geometric Lower Bound Theorem

Karim Adiprasito, Eran Nevo, José Alejandro Samper

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their toric varieties. The proof uses higher notions of chordality. Further, for C2-convex bodies, asymptotically tight lower bounds on the g-numbers of the approximating polytopes are given, in terms of their Hausdorff distance from the convex body.

Original languageEnglish (US)
Pages (from-to)359-378
Number of pages20
JournalGeometric and Functional Analysis
Volume26
Issue number2
DOIs
StatePublished - Apr 1 2016

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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