5,351 research outputs found
Complete Constant Mean Curvature surfaces in homogeneous spaces
In this paper we classify complete surfaces of constant mean curvature whose
Gaussian curvature does not change sign in a simply connected homogeneous
manifold with a 4-dimensional isometry group.Comment: We have corrected a mistake in Theorem 2.
Fatou's Theorem and minimal graphs
In this paper we extend a recent result of Collin-Rosenberg ({\it a solution
to the minimal surface equation in the Euclidean disc has radial limits almost
everywhere}) to a large class of differential operators in Divergence form.
Moreover, we construct an example (in the spirit of \cite{CR2}) of a minimal
graph in \mr, where \m is a Hadamard surface, over a geodesic disc which
has finite radial limits in a mesure zero set.Comment: 13 figure
Variational approach to second-order impulsive dynamic equations on time scales
The aim of this paper is to employ variational techniques and critical point
theory to prove some conditions for the existence of solutions to nonlinear
impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also
we will be interested in the solutions of the impulsive nonlinear problem with
linear derivative dependence satisfying an impulsive condition.Comment: 17 page
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