New constant mean curvature surfaces

M Kilian; I McIntosh; N Schmitt

New constant mean curvature surfaces

M Kilian, I McIntosh, N Schmitt

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We use the Dorfmeister-Pedit-Wu construction to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points With a Common tangent plane. An appendix, by the third author, describes the DPW potentials that appear to give CMC punctured spheres with k Delaunay ends (k-noids): the evidence is experimental at present. These can have both unduloidal and nodoidal ends.

Original language	English
Pages (from-to)	595-611
Number of pages	17
Journal	Experimental mathematics
Volume	9
Issue number	4
Publication status	Published - 2000

Keywords

HARMONIC MAPS

Cite this

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title = "New constant mean curvature surfaces",

abstract = "We use the Dorfmeister-Pedit-Wu construction to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points With a Common tangent plane. An appendix, by the third author, describes the DPW potentials that appear to give CMC punctured spheres with k Delaunay ends (k-noids): the evidence is experimental at present. These can have both unduloidal and nodoidal ends.",

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T1 - New constant mean curvature surfaces

AU - Kilian, M

AU - McIntosh, I

AU - Schmitt, N

PY - 2000

Y1 - 2000

N2 - We use the Dorfmeister-Pedit-Wu construction to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points With a Common tangent plane. An appendix, by the third author, describes the DPW potentials that appear to give CMC punctured spheres with k Delaunay ends (k-noids): the evidence is experimental at present. These can have both unduloidal and nodoidal ends.

AB - We use the Dorfmeister-Pedit-Wu construction to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points With a Common tangent plane. An appendix, by the third author, describes the DPW potentials that appear to give CMC punctured spheres with k Delaunay ends (k-noids): the evidence is experimental at present. These can have both unduloidal and nodoidal ends.

KW - HARMONIC MAPS

M3 - Article

SN - 1058-6458

VL - 9

SP - 595

EP - 611

JO - Experimental mathematics

JF - Experimental mathematics

IS - 4

ER -