A generalized affine isoperimetric inequality

DOI10.1007/BF02922171zbMath1069.52011arXivmath/0402083MaRDI QIDQ1768084

Xianqiang Yang

Publication date: 14 March 2005

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402083

zbMATH Keywords

affine isoperimetric inequality

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40)

Related Items

\(L_p\) Minkowski problem with not necessarily positive data ⋮ Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ The Christoffel problem in the hyperbolic plane ⋮ The two dimensional \(L_p\) Minkowski problem and nonlinear equations with negative exponents ⋮ STEADY STATES FOR ONE-DIMENSIONAL CURVATURE FLOWS ⋮ Variations on R. Schwartz's inequality for the Schwarzian derivative ⋮ One-dimensional conformal metric flow ⋮ On containment measure and the mixed isoperimetric inequality ⋮ Existence and uniqueness of solutions to Orlicz Minkowski problems involving \(0 < p < 1\) ⋮ Variational characterization for the planar dual Minkowski problem ⋮ The planar Orlicz Minkowski problem for \(p=0\) without even assumptions ⋮ The planar Orlicz Minkowski problem in the \(L^1\)-sense

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Extended affine surface area
• On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• On the uniqueness of stable ultimate shapes for the anisotropic curve-shortening problem
• The discrete planar \(L_0\)-Minkowski problem
• A direct proof of a theorem of Blaschke and Lebesgue.
• Bemerkungen zur Definition einer erweiterten Affinoberfläche von E. Lutwak. (Remarks on the definition of extended affine surface area given by E. Lutwak)
• On the regularity of solutions to a generalization of the Minkowski problem
• Equality of two representations of extended affine surface area
• A characterization of affine surface area
• On the \(L_{p}\) Minkowski problem for polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• On the Affine Surface Area
• The convex floating body.
• A general geometric construction for affine surface area
• Illumination bodies and affine surface area
• On the $L_{p}$-Minkowski problem
• Self-similar solutions for the anisotropic affine curve shortening problem