Rigidity of minimal hypersurfaces of spheres with constant Ricci curvature.
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
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
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...
Ruled W-surfaces in Minkowski 3-space
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.
Sechseckgewebe auf Flachen Positiver oder Negativer Krummung
Self-intersection Points in classical area-minimizing surfaces.
Sharp eigenvalue estimates of closed -hypersurfaces in locally symmetric spaces
The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.
Simons Type Equation in and and Applications
Let be an immersed surface in with constant mean curvature. We consider the traceless Weingarten operator associated to the second fundamental form of the surface, and we introduce a tensor , related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both and . By using these equations, we characterize some immersions for which or is appropriately bounded.
Size-minimizing rectifiable currents.
SO(2) invariant minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces.
Solutions positives d'équations elliptiques non linéaires avec exposant de Sobolev critique et conjecture de Rellich pour les surfaces à courbure moyenne prescrite
Solutions to the mean curvature equation by fixed point methods.
Some contributions to the differential geometry of submanifolds [Book]
Some existence and uniqueness theorems for doubly periodic minimal surfaces.
Some recent developments in the theory of properly embedded minimal surfaces in
Some remarkable properties of -graphs.
Some Results on Finiteness in Plateau's Problem, Part I.
Some Results on Finiteness in Plateau's Problem, Part II.
Some uniqueness and nonexistence theorems for embedded minimal surfaces.
Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations
On any space-like Weingarten surface in the three-dimensional Minkowski space we introduce locally natural principal parameters and prove that such a surface is determined uniquely up to motion by a special invariant function, which satisfies a natural non-linear partial differential equation. This result can be interpreted as a solution to the Lund-Regge reduction problem for space-like Weingarten surfaces in Minkowski space. We apply this theory to linear fractional space-like Weingarten surfaces...