Polyedrische 2-Mannigfaltigkeiten mit wenigen nicht-konvexen Ecken

Translated title of the contribution: Polyhedral 2-manifolds with few non-convex vertices

U. Betke, P. Gritzmann

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let P denote a polyhedral 2-manifold in ℝ3, i.e. a 2-dimensional cell-complex in ℝ3 whose underlying point-set is a closed connected 2-manifold. A vertex v of P is called convex if at least one of the two components into which P divides a sufficiently small ball centered at v is convex. It is shown that every polyhedral 2-manifold in ℝ3 of genus g>-1 contains at least five non-convex vertices and that for every positive integer g this bound is attained, i.e. there exists a polyhedral 2-manifold in ℝ3 of genus g with precisely five non-convex vertices.

Translated title of the contributionPolyhedral 2-manifolds with few non-convex vertices
Original languageGerman
Pages (from-to)1-21
Number of pages21
JournalMonatshefte fur Mathematik
Issue number1
StatePublished - Mar 1984
Externally publishedYes


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