相关论文: Constant mean curvature cylinders with irregular e…
We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a…
In the present paper we give a geometric proof for the existence of cylinders with constant mean curvature $H>H(X)$ in certain simply connected homogeneous three-manifolds $X$ diffeomorphic to $\mathbb{R}^3$, which always admit a Lie group…
We construct a new five parameter family of constant mean curvature trinoids with two asymptotically Delaunay ends and one irregular end.
In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the surface lies inside of the cylinder, we obtain some results of…
Shrinkers are special solutions of mean curvature flow (MCF) that evolve by rescaling and model the singularities. While there are infinitely many in each dimension, [CM1] showed that the only generic are round cylinders $\SS^k\times…
We prove the existence of a large class of initial data for the vacuum Einstein equations which possess a finite number of asymptotically Euclidean and asymptotically conformally cylindrical or periodic ends. Aside from being asymptotically…
We investigate CMC-surfaces with periodic metric in a dressing orbit of the cylinder. It is shown, that such surfaces are always of finite type. Using the periodicity conditions for the extended frame of a CMC-surface, we develop an…
We give a mathematical foundation for, and numerical demonstration of, the existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1 surface is…
We give a global version of the Bryant representation of surfaces of constant mean curvature one (cmc-1) in hyperbolic space. This allows to set the associated non-abelian period problem in the framework of flat unitary vector bundles on…
We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder $B(r)\times\R^{\ell}$ in a product Riemannian manifold $N^{n-\ell}\times\R^{\ell}$. It follows that a complete hypersurface of given constant…
We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the…
We show the existence of constant mean curvature surfaces in the homology classes of closed 3-manifolds.
The only non-compact linearly stable singularity models for mean curvature flow are cylindrical by Colding-Minicozzi. The uniqueness of blowups at singularities modeled on the cylinders has been established by the same authors. In this…
Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin$^c$ manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin$^c$ case the result of O.…
We propose a notion of stability for capillary hypersurfaces with constant higher order mean curvature and we generalize some results of the classical stability theory for CMC capillary hypersurfaces.
We use bifurcation theory to show the existence of infinite sequences isometric embeddings of tori with constant mean curvature (CMC) in Euclidean spheres that are not isometrically congruent to the CMC Clifford tori, and accumulating at…
We consider the monodromy problem of Darboux transforms of discrete isothermic surfaces using the integrable theory of discrete polarised curves. Then we provide, for the first time, closed-form discrete parametrisations of discrete…
We consider constant mean curvature surfaces of finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors in…
We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and…
In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations.…