Isolated singularities of the prescribed mean curvature equation in Minkowski 3-space

Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space

which gives an isometric embedding of the hyperbolic space H into R. Hano and Nomizu [11] were probably the first to observe the non-uniqueness of isometric embeddings of H in R by constructing other (geometrically distinct) entire solutions of (1.1)–(1.2) for n 1⁄4 2 (and c1 1) using methods of ordinary di¤erential equations. Using the theory of Monge-Ampère equations, A.-M. Li [12] studied en...

Constant Mean Curvature Surfaces in Euclidean and Minkowski 3-spaces

Spacelike constant mean curvature surfaces in Minkowski 3-space L have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for constant mean curvature surfaces in Euclidean space, replacing the group SU(2) with SU(1, 1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop grou...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

The Equation of Prescribed Ricci Curvature

Introduction. In [5], J. Milnor cited "understanding the Ricci tensor Rik = J^ Rt'kl 9J as a fundamental problem of present-day mathematics. A basic issue, then, is to determine which symmetric covariant tensors of rank two can be Ricci tensors of Riemannian metrics. The definition of Ricci curvature casts the problem of finding a metric g which realizes a given Ricci curvature R as one of solv...

Subharmonic solutions of the prescribed curvature equation∗

We study the existence of subharmonic solutions of the prescribed curvature equation − ( u′/ √ 1 + u′ )′ = f(t, u). According to the behaviour at zero, or at infinity, of the prescribed curvature f , we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations. 2010 Mathematics Subject Classification:...