The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry

  title={The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry},
  author={Kai-Seng Chou and Xu-jia Wang},
  journal={Advances in Mathematics},
Rotationally symmetric solutions to the L p -Minkowski problem
The $L_p$-Minkowski problem with super-critical exponents
The Lp-Minkowski problem deals with the existence of closed convex hypersurfaces in R with prescribed p-area measures. It extends the classical Minkowski problem and embraces several important
On the discrete Orlicz Minkowski problem
A flow method for the dual Orlicz–Minkowski problem
In this paper the dual Orlicz-Minkowski problem, a generalization of the $L_p$ dual Minkowski problem, is studied. By studying a flow involving the Gauss curvature and support function, we obtain a
Noncompact L_p-Minkowski problems
In this paper we prove the existence of complete, noncompact convex hypersurfaces whose $p$-curvature function is prescribed on a domain in the unit sphere. This problem is related to the solvability


On the _{}-Minkowski problem
A volume-normalized formulation of the Lp-Minkowski problem is presented. This formulation has the advantage that a solution is possible for all p > 1, including the degenerate case where the index p
The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem
The Brunn-Minkowski theory is the heart of quantitative convexity. It had its origins in Minkowski's joining his notion of mixed volumes with the Brunn-Minkowski inequality. One of Minkowski's major
Classification of limiting shapes for isotropic curve flows
with a 5 0, and initial condition x(p, 0) = xzo(p). This produces a family of curves yt = x(Si, t). Here n is the curvature, and n is the outward-pointing unit normal vector. These equations are
Motion of hypersurfaces by Gauss curvature
We consider n-dimensional convex Euclidean hypersurfaces moving with normal velocity proportional to a positive power α of the Gauss curvature. We prove that hypersurfaces contract to points in
Sharp Affine LP Sobolev Inequalities
A sharp affine Lp Sobolev inequality for functions on Euclidean n-space is established. This new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev
Self-similar solutions for the anisotropic affine curve shortening problem
Abstract. Similarity between the roles of the group $SL(2,\bf R)$ on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group of $S^2$ on
Partial Differential Equations Invariant under Conformal or Projective Transformations
A variational theory of the Hessian equation
By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of
A localization property of viscosity solutions to the Monge-Ampere equation and their strict convexity
The purpose of this note is to show a localization property of convex viscosity solutions to the Monge-Ampere inequality 0 1−(2/n)) are strictly convex