Monotone valuations on the space of convex functions

DOI10.1515/agms-2015-0012zbMath1321.26027arXiv1502.06729OpenAlexW1545607596MaRDI QIDQ2517394

Lorenzo Cavallina, Andrea Colesanti

Publication date: 18 August 2015

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.06729

zbMATH Keywords

convex functionsvaluationsconvex bodiesintrinsic volumessub-level sets

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)

Related Items (16)

Valuations on the Space of Quasi-Concave Functions ⋮ Real-valued valuations on Sobolev spaces ⋮ Fourier transform and valuations ⋮ Minkowski valuations under volume constraints ⋮ Laplace transforms and valuations ⋮ Translation invariant valuations on quasi-concave functions ⋮ A homogeneous decomposition theorem for valuations on convex functions ⋮ Geometric valuation theory ⋮ Minkowski valuations on convex functions ⋮ Equivariant endomorphisms of convex functions ⋮ Continuous valuations on the space of Lipschitz functions on the sphere ⋮ \(\mathrm{SL}(n)\) covariant vector-valued valuations on \(L^p\)-spaces ⋮ Hessian valuations ⋮ Valuations on log-concave functions ⋮ A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\) ⋮ The support of dually epi-translation invariant valuations on convex functions

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