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The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry
Abstract The L p -Minkowski problem introduced by Lutwak is solved for p ⩾ n + 1 in the smooth category. The relevant Monge–Ampere equation (0.1) is solved for all p > 1 . The same equation for p 1
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
The Curve Shortening Problem
BASIC RESULTS Short Time Existence Facts from Parabolic Theory Evolution of Geometric Quantities INVARIANT SOLUTIONS FOR THE CURVE SHORTENING FLOW Travelling Waves Spirals The Support Function of a
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
On quasilinear parabolic equations which admit global solutions for initial data with unrestricted growth
Abstract. Three classes of quasilinear parabolic equations which have the common feature that their principal coefficients decay as the solution or its gradient blows up are studied. Long time
A logarithmic Gauss curvature flow and the Minkowski problem
Abstract Let X 0 be a smooth uniformly convex hypersurface and f a postive smooth function in S n . We study the motion of convex hypersurfaces X (·, t ) with initial X (·,0)= θX 0 along its inner
Integrable Equations Arising from Motions of Plane Curves. II
  • K. Chou, C. Qu
  • Mathematics, Computer Science
    J. Nonlinear Sci.
  • 1 October 2003
TLDR
Inextensible motions and their associated integrable equations in all Klein geometries in the plane are determined and the relations between several pairs of these geometry provide a natural geometric explanation of the existence of transformations of Miura and Cole-Hopf type.
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