Establishes an additive kinematic formula for functional Minkowski vectors using mixed Monge-Ampère measures as the first integral-geometric application of their prior characterization.
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Continuous polynomial local functionals on convex functions admit integral representations via a finite family of polynomials, obtained by approximating from a classified dense subspace of smooth functionals using Goodey-Weil distributions.
Explicit representation formulas are derived for solutions to the Christoffel-Minkowski problem and related mixed Monge-Ampère and k-Hessian equations under rotational symmetry.
citing papers explorer
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Additive Kinematic Formulas for Functional Minkowski Vectors
Establishes an additive kinematic formula for functional Minkowski vectors using mixed Monge-Ampère measures as the first integral-geometric application of their prior characterization.
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Integral representation of polynomial local functionals on convex functions
Continuous polynomial local functionals on convex functions admit integral representations via a finite family of polynomials, obtained by approximating from a classified dense subspace of smooth functionals using Goodey-Weil distributions.
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Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
Explicit representation formulas are derived for solutions to the Christoffel-Minkowski problem and related mixed Monge-Ampère and k-Hessian equations under rotational symmetry.