1,571 research outputs found
Higher Genus Doubly Periodic Minimal Surfaces
We construct Weierstrass data for higher genus embedded doubly periodic minimal surfaces and present numerical evidence that the associated period problem can be solved. In the orthogonal ends case, there previously was only one known surface for each genus g. We illustrate multiple new examples for each genus g ≥ 3. In the parallel ends case, the known examples limit as a foliation of parallel planes with nodes. We construct a new example for each genus g ≥ 3 that limit as g−1 singly periodic Scherk surfaces glued between two doubly periodic Scherk surfaces and also as a singly periodic surface with four vertical and 2g horizontal Scherk ends. 2000 Mathematics Subject Classification. Primary 53A10; Secondary 49Q05, 53C42. Keywords: Minimal surfaces, doubly periodi
Saddle towers with infinitely many ends
We prove the existence of nonperiodic, properly embedded minimal surfaces in
with genus zero, infinitely many ends and one
limit end (in particular, they have infinite total curvature).Comment: 16 pages, 3 figure
An end-to-end-construction for singly periodic minimal surfaces
We show the existence of various families of properly embedded singly
periodic minimal surfaces in R^3 with finite arbitrary genus and Scherk type
ends in the quotient. The proof of our results is based on the gluing of small
perturbations of pieces of already known minimal surfaces.Comment: 49 page
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