Volume, polar volume and Euler characteristic for convex functions

DOI10.1016/j.aim.2019.01.012zbMath1429.52019arXiv1806.11084OpenAlexW2811172351MaRDI QIDQ1710400

Fabian Mussnig

Publication date: 22 January 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.11084

zbMATH Keywords

Euler characteristicconvex functionsvaluationstranslation invariance\(\mathrm{SL}(n)\) invariancepolar volume

Mathematics Subject Classification ID

Convex functions and convex programs in convex geometry (52A41) Convexity of real functions of several variables, generalizations (26B25) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Ordered topological linear spaces, vector lattices (46A40)

Related Items (14)

The Hadwiger theorem on convex functions. III: Steiner formulas and mixed Monge-Ampère measures ⋮ A homogeneous decomposition theorem for valuations on convex functions ⋮ Geometric valuation theory ⋮ The Hadwiger theorem on convex functions. IV: The Klain approach ⋮ Functional geominimal surface area and its related affine isoperimetric inequality ⋮ Monge-Ampère operators and valuations ⋮ Equivariant endomorphisms of convex functions ⋮ Continuous valuations on the space of Lipschitz functions on the sphere ⋮ SL\((n)\) covariant function-valued valuations ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ \(\mathrm{SL}(n)\) covariant vector-valued valuations on \(L^p\)-spaces ⋮ Valuations on log-concave functions ⋮ The support of dually epi-translation invariant valuations on convex functions ⋮ A Riesz representation theorem for functionals on log-concave functions

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