Geometric valuation theory

DOI10.4171/8ecm/25zbMath1528.52008arXiv2111.09024OpenAlexW3214548053MaRDI QIDQ6064556

Monika Ludwig

Publication date: 10 November 2023

Published in: European Congress of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.09024

zbMATH Keywords

convex functionconvex bodyvaluationSobolev space.

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) 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)

Cites Work

• A valuation-theoretic approach to translative-equidecomposability
• Real-valued valuations on Sobolev spaces
• Spin-invariant valuations on the octonionic plane
• Laplace transforms and valuations
• Covariance matrices and valuations
• The affine Sobolev-Zhang inequality on BV(\(\mathbb R^n)\)
• Classification of invariant valuations on the quaternionic plane
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Minkowski areas and valuations
• Projection bodies in complex vector spaces
• Weakly continuous valuations on convex polytopes
• Fisher information and matrix-valued valuations
• Hermitian integral geometry
• Invariant valuations on star-shaped sets
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Difference bodies in complex vector spaces
• Minkowski valuations intertwining the special linear group
• Extended affine surface area
• Plurisubharmonic functions on the octonionic plane and \(Spin (9)\)-invariant valuations on convex sets
• Orlicz centroid bodies
• A Hadwiger-type theorem for the special unitary group
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Über einige Eigenschaften der Affinoberfläche beliebiger konvexer Körper. (On some properties of the affine surface area of arbitrary convex bodies)
• Intersection bodies and dual mixed volumes
• Continuous translation invariant valuations on the space of compact convex sets
• Description of continuous isometry covariant valuations on convex sets
• A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\)
• Continuous rotation invariant valuations on convex sets
• Continuous valuations on convex sets
• Ellipsoids and matrix-valued valuations
• Upper semicontinuous valuations on the space of convex discs
• A new ellipsoid associated with convex bodies
• On P. McMullen's conjecture on translation invariant valuations
• The affine Sobolev inequality.
• \(L_ p\) affine isoperimetric inequalities.
• Minkowski valuations and generalized valuations
• Minkowski valuations on convex functions
• Volume, polar volume and Euler characteristic for convex functions
• \(\mathrm{SL}(m, \mathbb{C})\)-equivariant and translation covariant continuous tensor valuations
• Continuity and representation of valuations on star bodies
• Minkowski valuations on lattice polytopes
• Integral geometry under \(G_2\) and \(Spin(7)\)
• The Cramer-Rao inequality for star bodies
• Valuations on polytopes containing the origin in their interiors
• Projection bodies and valuations
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• A characterization of affine surface area
• A characterization of affine length and asymptotic approximation of convex discs
• Centro-affine tensor valuations
• Valuations on log-concave functions
• The support of dually epi-translation invariant valuations on convex functions
• A homogeneous decomposition theorem for valuations on convex functions
• Dimension of the space of unitary equivariant translation invariant tensor valuations
• Continuous valuations on the space of Lipschitz functions on the sphere
• SL\((n)\) covariant function-valued valuations
• Dual mixed volumes
• A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\)
• Valuations on convex functions and convex sets and Monge-Ampère operators
• \(L_p\)-Minkowski valuations on \(L^q\)-spaces
• Radial continuous valuations on star bodies
• Local tensor valuations
• Valuation theory of indefinite orthogonal groups
• Tensor valuations on lattice polytopes
• Hadwiger's theorem for definable functions
• The module of unitarily invariant area measures
• Valuations and surface area measures
• Valuations on convex sets, non-commutative determinants, and pluripotential theory
• Convex valuations invariant under the Lorentz group
• Monotone valuations on the space of convex functions
• Vektorielle Integralgeometrie
• \(L_{p}\) Minkowski valuations on polytopes
• Radial continuous rotation invariant valuations on star bodies
• Beweis eines Funktionalsatzes für konvexe Körper
• Additive Funktionale \(k\)-dimensionaler Eikörper. I
• Minkowski valuations on $L^{p}$-spaces
• Valuations on Sobolev spaces
• Invariant valuations on quaternionic vector spaces
• Algebraic Integral Geometry
• Semi-Valuations on $BV(\\mathbb R^n)$
• Moments and valuations
• Blaschke valuations
• Valuations on Lp-Spaces
• $\mathrm{GL}(n)$ contravariant Minkowski valuations
• On the Affine Surface Area
• The Centro-Affine Hadwiger Theorem
• Hessian valuations
• Intersection bodies and valuations
• A characterization of Lp intersection bodies
• Star body valued valuations
• The convex floating body.
• Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
• Translation invariant valuations on quasi-concave functions
• Introduction to the Theory of Valuations
• SL($n$) covariant vector valuations on polytopes
• Equivariant Endomorphisms of the Space of Convex Bodies
• A short proof of Hadwiger's characterization theorem
• Simple valuations on convex bodies
• $GL(n)$ equivariant Minkowski valuations
• Orlicz valuations
• Valuations on Banach Lattices
• Moment Matrices and SL(n) Equivariant Valuations on Polytopes
• Invariant Valuations on Super-Coercive Convex Functions
• Valuations on Convex Functions
• Minkowski Valuations in a 2-Dimensional Complex Vector Space
• 𝐿_{𝑝}-Blaschke valuations
• Rotation Invariant Valuations
• Valuations on Lattice Polytopes
• Convex and Discrete Geometry
• Kinematic formulas on the quaternionic plane
• $\mathrm {SL}(n)$-contravariant $L_p$-Minkowski valuations
• Convex Bodies The Brunn-MinkowskiTheory
• Theory of Valuations on Manifolds, IV. New Properties of the Multiplicative Structure
• Minkowski valuations
• Optimal Sobolev norms and the Lp Minkowski problem
• Affine Function-Valued Valuations
• LYZ Matrices and SL() Contravariant Valuations on Polytopes
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture
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