Constant mean curvature surfaces and loop groups.
Constant mean curvature surfaces bounded by a circle.
Constant mean curvature surfaces constructed by fusing Wente tori.
Constant mean curvature surfaces in -space forms
Constant mean curvature surfaces with two ends in hyperbolic space.
Constant mean curvature tori in terms of elliptic functions.
Constant Mean Curvature Tori with spherical curvature lines in noneuclidean geometry.
Constant scalar curvature hypersurfaces with spherical boundary in Euclidean space.
It is still an open question whether a compact embedded hypersurface in the Euclidean space with constant mean curvature and spherical boundary is necessarily a hyperplanar ba1l or a spherical cap, even in the simplest case of a compact constant mean curvature surface in R3 bounded by a circle. In this paper we prove that this is true for the case of the scalar curvature. Specifica1ly we prove that the only compact embedded hypersurfaces in the Euclidean space with constant scalar curvature and...
Constructing isothermal curvature line coordinates on surfaces which admit them
Isothermic parameterizations are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.
Construction de surfaces à courbure moyenne constante
Construction de surfaces minimales en recollant des surfaces de Scherk
On construit des surfaces minimales simplement périodiques dans l’espace euclidien de dimension 3 en recollant des surfaces de Scherk et en utilisant les techniques de Kapouleas.
Construction of compact constant mean curvature hypersurfaces with topology
In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.
Continuity Estimates for Solutions to the Prescribed-Curvature Dirichlet Problem.
Continuity of Minimal Surfaces with Piecewise Smooth Free Boundaries.
Convex Hulls of Complete Minimal Surfaces.
Correction to: Stabel Minimal Surfaces and Spatial Topology in General Relativity.
Counterexamples to the conjecture on minimal S2 in CPn with constant Kaehler angle.
Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow
Curvature Estimates for Immersions of Minimal Surface Type via Uniformization and Theorems of Bernstein Type.
Curvature estimates for minimal hypersurfaces in singular spaces.