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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Curvature estimates for minimal surfaces with total boundary curvature less than 4$ \pi$


Author: Giuseppe Tinaglia
Journal: Proc. Amer. Math. Soc. 137 (2009), 2445-2450
MSC (2000): Primary 53A10
DOI: https://doi.org/10.1090/S0002-9939-09-09810-4
Published electronically: February 6, 2009
MathSciNet review: 2495281
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Abstract: We establish a curvature estimate for classical minimal surfaces with total boundary curvature less than 4$ \pi$. The main application is a bound on the genus of these surfaces depending solely on the geometry of the boundary curve. We also prove that the set of simple closed curves with total curvature less than $ 4\pi$ and which do not bound an orientable compact embedded minimal surface of genus greater than $ g$, for any given $ g$, is open in the $ C^{2,\alpha}$ topology.


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Additional Information

Giuseppe Tinaglia
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-4618
Email: giuseppetinaglia@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-09-09810-4
Received by editor(s): March 21, 2008
Received by editor(s) in revised form: October 20, 2008
Published electronically: February 6, 2009
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.