Uniform approximation by complete minimal surfaces of finite total curvature in $\mathbb {R}^3$
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- by Francisco J. López PDF
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Abstract:
We prove that any compact minimal surface in $\mathbb {R}^3$ can be uniformly approximated by complete minimal surfaces of finite total curvature in $\mathbb {R}^3$. This Mergelyan type result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on regions of finite conformal type. We deal only with the orientable case.References
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Additional Information
- Francisco J. López
- Affiliation: Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 - Granada, Spain
- Email: fjlopez@ugr.es
- Received by editor(s): April 29, 2012
- Published electronically: July 15, 2014
- Additional Notes: This research was partially supported by MCYT-FEDER research projects MTM2007-61775 and MTM2011-22547, and Junta de Andalucía Grant P09-FQM-5088
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 366 (2014), 6201-6227
- MSC (2010): Primary 53A10; Secondary 49Q05, 49Q10, 53C42
- DOI: https://doi.org/10.1090/S0002-9947-2014-05890-X
- MathSciNet review: 3267008