Deforming a hypersurface by principal radii of curvature and support function

DOI10.1007/s00526-018-1462-3zbMath1403.53057arXiv1803.08470OpenAlexW2963386785WikidataQ128875987 ScholiaQ128875987MaRDI QIDQ1630854

Mohammad N. Ivaki

Publication date: 5 December 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.08470

zbMATH Keywords

elementary symmetric polynomialChristoffel-Minkowski problemhomothetic self-similar solutionspherical Hessian

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Deforming a hypersurface by Gauss curvature and support function
• Contracting convex hypersurfaces by curvature
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Four-manifolds with positive curvature operator
• Expansion of convex hypersurfaces by nonhomogeneous functions of curvature
• An expansion of convex hypersurfaces
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• A unified flow approach to smooth, even \(L_p\)-Minkowski problems
• Asymptotic behavior of flows by powers of the Gaussian curvature
• \(L^p\) Christoffel-Minkowski problem: the case \(1< p<k+1\)
• Sharp affine \(L_ p\) Sobolev inequalities.
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the regularity of solutions to a generalization of the Minkowski problem
• Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Symmetries of surfaces of constant width
• Intermediate Christoffel-Minkowski problems for figures of revolution
• Non-scale-invariant inverse curvature flows in Euclidean space
• The planar Busemann-Petty centroid inequality and its stability
• A Fourier transform approach to Christoffel’s problem
• On the regularity of the solution of then-dimensional Minkowski problem
• Convex Bodies The Brunn-MinkowskiTheory
• The determination of convex bodies from their mean radius of curvature functions
• Christoffel's problem for general convex bodies

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