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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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.Expand