The logarithmic Minkowski problem
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Publication:4924068
DOI10.1090/S0894-0347-2012-00741-3zbMath1272.52012OpenAlexW2149194571MaRDI QIDQ4924068
Erwin Lutwak, Deane Yang, Gaoyong Zhang, Károly jun. Böröczky
Publication date: 30 May 2013
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0894-0347-2012-00741-3
normed spaceLebesgue measure\(L_p\)-Minkowski problemcone-volume measureMinkowski problemAleksandrov bodylogarithmic Minkowski problem
Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(\mathrm{SL}(n)\) invariant valuations on polytopes
- The Minkowski problem for polytopes
- Extremum problems for the cone volume functional of convex polytopes
- An asymmetric affine Pólya-Szegő principle
- The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
- Projection problems for symmetric polytopes
- Concentration of mass on convex bodies
- Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
- General affine surface areas
- The even Orlicz Minkowski problem
- General \(L_{p}\) affine isoperimetric inequalities
- Affine Moser-Trudinger and Morrey-Sobolev inequalities
- Deforming convex hypersurfaces by the \(n\)th root of the Gaussian curvature
- The heat equation shrinking convex plane curves
- A Minkowski problem for electrostatic capacity
- Blaschke-Santaló inequalities
- The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
- Ellipsoids and matrix-valued valuations
- On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
- On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
- A new ellipsoid associated with convex bodies
- The \(L^p\)-Busemann-Petty centroid inequality
- The discrete planar \(L_0\)-Minkowski problem
- The affine Sobolev inequality.
- \(L_ p\) affine isoperimetric inequalities.
- A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
- Sharp affine \(L_ p\) Sobolev inequalities.
- Gauss curvature flow: The fate of the rolling stones
- The Cramer-Rao inequality for star bodies
- Convex hypersurfaces of prescribed curvatures
- Projecting the surface measure of the sphere of \({\ell}_p^n\)
- On the Christoffel-Minkowski problem of Firey's \(p\)-sum
- On the regularity of solutions to a generalization of the Minkowski problem
- \(L_p\) Minkowski problem with not necessarily positive data
- Asymmetric affine \(L_p\) Sobolev inequalities
- On the \(L_{p}\) Minkowski problem for polytopes
- Volume inequalities for subspaces of \(L_p\)
- The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
- Polar correspondence with respect to a convex region
- Centro-Affine Invariants for Smooth Convex Bodies
- The Minkowski problem for the torsional rigidity
- Relative entropy of cone measures and L p centroid bodies
- The surface measure and cone measure on the sphere of ℓ_{𝑝}ⁿ
- Deforming a hypersurface by its Gauss-Kronecker curvature
- Shapes of worn stones
- On the regularity of the solution of then-dimensional Minkowski problem
- Affine inequalities and radial mean bodies
- The Brunn-Minkowski inequality
- Classification of limiting shapes for isotropic curve flows
- On the $L_{p}$-Minkowski problem
- Remarks on the 2-Dimensional Lp-Minkowski Problem
- Convex and Discrete Geometry
- Optimal Sobolev norms and the Lp Minkowski problem
- On Differential Geometry in the Large, I (Minkowski's Problem)
- The Weyl and Minkowski problems in differential geometry in the large