Delaunay Ends of Constant Mean Curvature Surfaces
نویسندگان
چکیده
We use the generalized Weierstrass representation to analyze the asymptotic behavior of a constant mean curvature surface that locally arises from an ODE with a regular singularity. We show that if system is a perturbation of that of a Delaunay surface, then the corresponding constant mean curvature surface has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal.
منابع مشابه
Constant Mean Curvature Surfaces of Any Positive Genus
We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus g ≥ 1, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.
متن کاملTriunduloids: Embedded Constant Mean Curvature Surfaces with Three Ends and Genus Zero
In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; they are classified using their asymptotic necksizes. We work in a class slightl...
متن کاملConstant Mean Curvature Surfaces with Delaunay Ends in 3-dimensional Space Forms
This paper presents a unified treatment of constant mean curvature (cmc) surfaces in the simply-connected 3-dimensional space forms R, S and H in terms of meromorphic loop Lie algebra valued 1-forms. We discuss global issues such as period problems and asymptotic behaviour involved in the construction of cmc surfaces with nontrivial topology. We prove existence of new examples of complete non-s...
متن کاملConstant mean curvature surfaces with Delaunay ends
In this paper we shall present a construction of Alexandrov-embedded complete surfaces M in R with nitely many ends and nite topology, and with nonzero constant mean curvature (CMC). This construction is parallel to the well-known original construction by Kapouleas [3], but we feel that ours somewhat simpler analytically, and controls the resulting geometry more closely. On the other hand, the ...
متن کاملRolling Construction for Anisotropic Delaunay Surfaces
Anisotropic Delaunay surfaces are surfaces of revolution with constant anisotropic mean curvature. We show how the generating curves of such surfaces can be obtained as the trace of a point held in a fixed position relative to a curve which is rolled without slipping along a line. This generalizes the classical construction for surfaces of revolution with constant mean curvature due to Delaunay...
متن کامل