7,593 research outputs found
Coplanar constant mean curvature surfaces
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 arXiv:math.DG/0102183. Here we extend the arguments to the case of an
arbitrary number of ends, under the assumption that the asymptotic axes of the
ends lie in a common plane: we construct and classify the entire family of
these genus-zero coplanar constant mean curvature surfaces.Comment: 35 pages, 10 figures; minor revisions including one new figure; to
appear in Comm. Anal. Geo
Triunduloids: 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 slightly more general than embedded surfaces, namely immersed
surfaces which bound an immersed three-manifold, as introduced by Alexandrov.Comment: LaTeX, 22 pages, 2 figures (8 ps files); full version of our
announcement math.DG/9903101; final version (minor revisions) to appear in
Crelle's J. reine angew. Mat
Constant mean curvature surfaces with three ends
We announce the classification of complete, almost embedded surfaces of
constant mean curvature, with three ends and genus zero: they are classified by
triples of points on the sphere whose distances are the asymptotic necksizes of
the three ends.Comment: LaTex, 4 pages, 1 postscript figur
On Finite 4D Quantum Field Theory in Non-Commutative Geometry
The truncated 4-dimensional sphere and the action of the
self-interacting scalar field on it are constructed. The path integral
quantization is performed while simultaneously keeping the SO(5) symmetry and
the finite number of degrees of freedom. The usual field theory UV-divergences
are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove
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