How do difference bodies in complex vector spaces look like? A geometrical approach

DOI10.1142/S0219199714500230zbMath1321.52004arXiv1602.00960MaRDI QIDQ5264559

Eugenia Saorín Gómez, Judit Abardia-Evéquoz

Publication date: 27 July 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00960

zbMATH Keywords

volumespherical harmonicdimensionpolytopeconvex bodyMinkowski valuationcomplex difference body

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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Cites Work

• Successive radii and Minkowski addition
• Projection bodies in complex vector spaces
• Hermitian integral geometry
• Difference bodies in complex vector spaces
• The difference body of a convex body
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
• Projection bodies and valuations
• Annihilating properties of convolution operators on complex spheres
• The module of unitarily invariant area measures
• The complex Busemann-Petty problem on sections of convex bodies
• Structure of the unitary valuation algebra
• Comparison of volumes of convex bodies in real, complex, and quaternionic spaces
• Zur Addition beweglicher ebener Eibereiche
• Complex intersection bodies
• Distributions and Valuations
• Rotation Invariant Minkowski Classes of Convex Bodies
• The Addition Formula for Jacobi Polynomials and Spherical Harmonics
• Orthogonal Bases for Spaces of Complex Spherical Harmonics
• Minkowski valuations