Curvature estimates for minimal surfaces with total boundary curvature less than 4
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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We establish a curvature estimate for classical minimal surfaces with total boundary curvature less than 4. 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
and which do not bound an orientable compact embedded minimal surface of genus greater than
, for any given
, is open in the
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.