A Fourier transform approach to Christoffel’s problem

DOI10.1090/S0002-9947-2011-05267-0zbMath1234.52007OpenAlexW1982312698MaRDI QIDQ3103846

Maryna Yaskina, Vladyslav Yaskin, Paul R. Goodey

Publication date: 12 December 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2011-05267-0

zbMATH Keywords

Fourier transformChristoffel problemfirst surface area measureregularity of integral transformsspherical kernel

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Inequalities and extremum problems involving convexity in convex geometry (52A40) Spherical harmonics (33C55)

Related Items

Projection functions, area measures and the Alesker-Fourier transform ⋮ Deforming a hypersurface by principal radii of curvature and support function ⋮ Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems ⋮ The Christoffel problem by the fundamental solution of the Laplace equation

Cites Work

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• Convex hypersurfaces of prescribed Weingarten curvatures
• Centrally symmetric convex bodies and the spherical Radon transform
• Generalized intersection bodies
• On surface area measures of convex bodies
• Das Christoffel-Problem für Polytope
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• Convex hypersurfaces of prescribed curvatures
• The Christoffel-Minkowski problem. II: Weingarten curvature equations
• Fourier transforms and the Funk-Hecke theorem in convex geometry
• Stability results for convex bodies in geometric tomography
• Manifolds with preassigned curvature—a survey
• On the regularity of the solution of then-dimensional Minkowski problem
• The Christofel‐Minkowski problem III: Existence and convexity of admissible solutions
• The determination of convex bodies from their mean radius of curvature functions
• Christoffel's problem for general convex bodies