Transactions of the American Mathematical Society

Author(s): Francisco J. López
Journal: Trans. Amer. Math. Soc. 356 (2004), 703-733.
MSC (2000): Primary 53A10; Secondary 53C42
Posted: August 25, 2003
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Abstract: This paper deals with the study of those closed subsets $F \subset \mathbb{R} ^3$ for which the following statement holds:

is a properly immersed minimal surface in $\mathbb{R} ^3$ of finite topology that is eventually disjoint from

then

has finite total curvature.

The same question is also considered when the conclusion is finite type or parabolicity.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53A10, 53C42

Francisco J. López
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email: fjlopez@goliat.ugr.es

DOI: 10.1090/S0002-9947-03-03213-6
PII: S 0002-9947(03)03213-6
Keywords: Properly immersed minimal surfaces, finite topology, finite total curvature
Received by editor(s): November 29, 2001
Received by editor(s) in revised form: September 17, 2002
Posted: August 25, 2003
Additional Notes: The author's research was partially supported by MCYT-FEDER grant number BFM2001-3489.
Copyright of article: Copyright 2003, American Mathematical Society

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