Valuations on convex functions and convex sets and Monge-Ampère operators

DOI10.1515/advgeom-2018-0031zbMath1445.52011arXiv1703.08778OpenAlexW2963014222MaRDI QIDQ2322402

Semyon Alesker

Publication date: 4 September 2019

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

Full work available at URL: https://arxiv.org/abs/1703.08778

zbMATH Keywords

Monge-Ampère operatorvaluations and convex functions

Mathematics Subject Classification ID

Dissections and valuations (Hilbert's third problem, etc.) (52B45) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Related Items (16)

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 ⋮ Minkowski valuations on convex functions ⋮ The Hadwiger theorem on convex functions. IV: The Klain approach ⋮ Monge-Ampère operators and valuations ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Equivariant endomorphisms of convex functions ⋮ Dimension of the space of unitary equivariant translation invariant tensor valuations ⋮ 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 ⋮ A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\) ⋮ 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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