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In this article, we study the ramification of the Gauss map of complete minimal surfaces in and on annular ends. We obtain results which are similar to the ones obtained by Fujimoto ([4], [5]) and Ru ([13], [14]) for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. We thus give an improvement...
We study the ramification of the Gauss map of complete minimal surfaces in on annular ends. This is a continuation of previous work of Dethloff-Ha (2014), which we extend here to targets of higher dimension.
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
This article discusses the numerical approximation of
time dependent Ginzburg-Landau equations. Optimal
error estimates which are robust with respect
to a large Ginzburg-Landau parameter are established for a
semi-discrete in time and a fully discrete approximation
scheme. The proofs rely on an asymptotic
expansion of the exact solution and a stability result
for degree-one Ginzburg-Landau vortices. The error bounds
prove that degree-one vortices can be approximated robustly
while unstable higher...
In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set , where and are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.
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