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Ramification of the Gauss map of complete minimal surfaces in $ℝ^{3}$ and $ℝ^{4}$ on annular ends

Gerd Dethloff, Pham Hoang Ha (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

In this article, we study the ramification of the Gauss map of complete minimal surfaces in $ℝ^{3}$ and $ℝ^{4}$ 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...

Ramification of the Gauss map of complete minimal surfaces in $ℝ^{m}$ on annular ends

Gerd Dethloff, Pham Hoang Ha, Pham Duc Thoan (2016)

Colloquium Mathematicae

We study the ramification of the Gauss map of complete minimal surfaces in $ℝ^{m}$ on annular ends. This is a continuation of previous work of Dethloff-Ha (2014), which we extend here to targets of higher dimension.

Regolarità di frontiere minimali con ostacoli sottili

Mimma de Acutis (1979)

Rendiconti del Seminario Matematico della Università di Padova

Régularité des hypersurfaces minimales

Enrico Bombieri (1968/1969)

Séminaire Bourbaki

Regularity and Finiteness of Solutions to the Free Boundary Problem for Minimal Surfaces.

Friedrich Tomi, Hans W. Alt (1985)

Mathematische Zeitschrift

Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space.

R. Hardt, F.-H. Lin (1987)

Inventiones mathematicae

Regularity of a Minimal Surface at its Free Boundary.

Rugang Ye (1988)

Mathematische Zeitschrift

Regularity of weak H-surfaces.

Michael Grüter (1981)

Journal für die reine und angewandte Mathematik

Regularity results for minimizing currents with a free boundary.

Michael Grüter (1987)

Journal für die reine und angewandte Mathematik

Remarks on the Darboux transform of isothermic surfaces.

Hertrich-Jeromin, Udo, Pedit, Franz (1997)

Documenta Mathematica

Remarks on the Isoperimetric Inequality for Multiply-connected H-Surfaces.

Helmut Kaul (1972)

Mathematische Zeitschrift

Remarks on the Stability of Minimal Submanifolds of IRn.

Joel Spruck (1975)

Mathematische Zeitschrift

Rigidity of minimal hypersurfaces of spheres with constant Ricci curvature.

Perdomo, Oscar (2004)

Revista Colombiana de Matemáticas

Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices

Sören Bartels (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices

Sören Bartels (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Ruled W-surfaces in Minkowski 3-space $ℜ_{1}^{3}$

Rashad A. Abdel-Baky, H. N. Abd-Ellah (2008)

Archivum Mathematicum

In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set ${K, K_{I I}, H, H_{I I}}$ , where $(K, H)$ and $(K_{I I}, H_{I I})$ 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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