Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Uniform approximation by complete minimal surfaces of finite total curvature in $ \mathbb{R}^3$


Author: Francisco J. López
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
Published electronically: July 15, 2014
MathSciNet review: 3267008
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53A10, 49Q05, 49Q10, 53C42

Retrieve articles in all journals with MSC (2010): 53A10, 49Q05, 49Q10, 53C42


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-2014-05890-X
Keywords: Complete minimal surfaces of finite total curvature, compact minimal surfaces, Runge's theorem, Mergelyan's theorem
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
Article copyright: © Copyright 2014 American Mathematical Society