Valuations on Convex Functions
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Publication:5243350
DOI10.1093/imrn/rnx189zbMath1436.52014arXiv1703.06455OpenAlexW2604718561MaRDI QIDQ5243350
Monika Ludwig, Fabian Mussnig, Andrea Colesanti
Publication date: 18 November 2019
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.06455
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)
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The Hadwiger theorem on convex functions. III: Steiner formulas and mixed Monge-Ampère measures ⋮ The Löwner function of a log-concave function ⋮ A homogeneous decomposition theorem for valuations on convex functions ⋮ Geometric valuation theory ⋮ The Hadwiger theorem on convex functions. IV: The Klain approach ⋮ Equivariant endomorphisms of convex functions ⋮ Volume, polar volume and Euler characteristic for convex functions ⋮ Dimension of the space of unitary equivariant translation invariant tensor valuations ⋮ Continuous valuations on the space of Lipschitz functions on the sphere ⋮ Invariant Valuations on Super-Coercive Convex Functions ⋮ \(\mathrm{SL}(n)\) covariant vector-valued valuations on \(L^p\)-spaces ⋮ \(\mathrm{SL}(m, \mathbb{C})\)-equivariant and translation covariant continuous tensor valuations ⋮ 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 ⋮ A Riesz representation theorem for functionals on log-concave functions ⋮ Affine invariant maps for log-concave functions
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