Multiplicity results for the assigned Gauss curvature problem in R

Associated to any solution of the super-Liouville system is a holomorphic quadratic differential T (z), and when our boundary condition is satisfied, T becomes real on the boundary..

We refer to the papers [17,18] for the case of non-negative solutions and subcritical values of the exponent p (see also [2,4]) and to the works [14,15] for the case of

∂Ω with negative outward normal derivatives, it is not difficult to construct, by the same method as for Theorem 1.4, a family of solutions such that a single bubble appears near

careful study of this flow, we shall give another proof of the Minkowski problem in the smooth category..

First the wave packet method for approximating solutions of the Schrödinger equation (see for example [7] and [17], or [3] for a generalized notion of wave packet) that we will

For an arbitrary convex body, the Gauss curvature measure is defined as the push-forward of the uniform measure σ on the sphere using the inverse of the Gauss map G : ∂Ω −→ S m

In this paper, we consider the problem of prescribing the Gauss curvature (in a generalised measure-theoretic sense) of convex sets in the Minkowski spacetime.. This problem is

To complete the proof of the existence part of Alexandrov’s theorem, it remains to show that, given a solution (φ, ψ) of Kantorovitch’s variational problem, the Gauss curvature