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Polyhedron Theorems for Non‐Smooth Cell Complexes
Author(s) -
Zähle M.
Publication year - 1987
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19871310124
Subject(s) - polyhedron , mathematics , curvature , pure mathematics , boundary (topology) , function (biology) , unit (ring theory) , mathematical analysis , combinatorics , geometry , mathematics education , evolutionary biology , biology
Results like E ULER'S polyhedron theorem or relations for the E ULER characteristic are extended to signed curvature measures of p ‐dimensional topological polyhedra in R d . The cells are assumed to be finite unions of compact manifolds with boundary and positive reach. By means of generalized unit normal bundles and generalized principal curvatures provided with a certain set additive index function the global problems can be reduced to local variants.