Curvature estimates for minimal surfaces with total boundary curvature less than 4$\pi$
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- by Giuseppe Tinaglia PDF
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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.References
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2445-2450
- MSC (2000): Primary 53A10
- DOI: https://doi.org/10.1090/S0002-9939-09-09810-4
- MathSciNet review: 2495281