Properly immersed minimal disks bounded by straight lines |
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| Authors: | Francisco J. López Fusheng Wei |
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| Affiliation: | (1) Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071–Granada, Spain (e-mail:filopez@goliat.ugr.es), ES;(2) Departement of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061–0123, USA (e-mail: fwei@math.vt.edu), US |
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| Abstract: | Let and be two distinct parallel planes in . Let and denote two points such that the segment meets and orthogonally. Let be a straight line containing , and denote as the set of straight lines in containing . Then there exists an analytic family of proper pairwise non congruent minimal immersions satisfying: 1. is homeomorphic to , where 2. , where . 3. is contained in the slab determined by and . 4. If and are the two connected components of , then is injective, . 5. The parameter is an analytic determination of the angle that the orthogonal projection of on makes with and is invariant under the reflection around a straight line not contained in the surface. 6. If is a proper minimal immersion satisfying 1, 2, 3 and4, then, up to a rigid motion, . Received December 28, 1997 / Revised November 20, 1999 / Published online October 11, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 53A10 53C42 |
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