Weakly continuous valuations on convex polytopes

DOI10.1007/BF01198585zbMath0526.52003OpenAlexW2006803121MaRDI QIDQ595200

Peter McMullen

Publication date: 1983

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01198585

zbMATH Keywords

Minkowski sumcovariant valuationstranslation invariant valuation

Mathematics Subject Classification ID

Other problems of combinatorial convexity (52A37) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Polytopes and polyhedra (52Bxx)

Related Items (18)

Valuations on Convex Bodies: The Classical Basic Facts ⋮ A valuation-theoretic approach to translative-equidecomposability ⋮ The zonoid algebra, generalized mixed volumes, and random determinants ⋮ Translative integral formulae for convex bodies ⋮ Cycles representing the Todd class of a toric variety ⋮ An algebraic construction of sum-integral interpolators ⋮ On the inverse Klain map ⋮ Geometric valuation theory ⋮ On the extendability by continuity of angular valuations on polytopes ⋮ On extendability by continuity of valuations on convex polytopes ⋮ Flag Measures for Convex Bodies ⋮ EXTENSIONS OF TRANSLATION INVARIANT VALUATIONS ON POLYTOPES ⋮ Local formulas for Ehrhart coefficients from lattice tiles ⋮ Valuations on log-concave functions ⋮ The polytope algebra ⋮ Continuous translation invariant valuations on convex bodies ⋮ Valuations and Tensor Weights on Polytopes ⋮ Integral geometry of translation invariant functionals. I: The polytopal case

Cites Work

• Lattice invariant valuations on rational polytopes
• Translationsinvariante, additive und schwachstetige Polyederfunktionale
• Non-linear angle-sum relations for polyhedral cones and polytopes
• Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
• The algebra of polytopes in affine spaces.
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