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15 June 2005 Complete proper minimal surfaces in convex bodies of 3
Francisco Martín, Santiago Morales
Duke Math. J. 128(3): 559-593 (15 June 2005). DOI: 10.1215/S0012-7094-04-12835-0

Abstract

Consider a convex domain B of 3 . We prove that there exist complete minimal surfaces that are properly immersed in B . We also demonstrate that if D and D ' are convex domains with D bounded and the closure of D contained in D ' , then any minimal disk whose boundary lies in the boundary of D can be approximated in any compact subdomain of D by a complete minimal disk that is proper in D ' . We apply these results to study the so-called type problem for a minimal surface: we demonstrate that the interior of any convex region of 3 is not a universal region for minimal surfaces, in the sense explained by Meeks and Pérez in [9].

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Francisco Martín. Santiago Morales. "Complete proper minimal surfaces in convex bodies of 3 ." Duke Math. J. 128 (3) 559 - 593, 15 June 2005. https://doi.org/10.1215/S0012-7094-04-12835-0

Information

Published: 15 June 2005
First available in Project Euclid: 9 June 2005

zbMATH: 1082.53009
MathSciNet: MR2145744
Digital Object Identifier: 10.1215/S0012-7094-04-12835-0

Subjects:
Primary: 53A10
Secondary: 49Q05, 49Q10, 53C42

Rights: Copyright © 2005 Duke University Press

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Vol.128 • No. 3 • 15 June 2005
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