Journal of Differential Geometry

Local removable singularity theorems for minimal laminations

William H. Meeks, Joaquín Pérez, and Antonio Ros

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Abstract

In this paper we prove a local removable singularity theorem for certain minimal laminations with isolated singularities in a Riemannian three-manifold. This removable singularity theorem is the key result used in our proof that a complete, embedded minimal surface in $\mathbb{R}^3$ with quadratic decay of curvature has finite total curvature.

Article information

Source
J. Differential Geom., Volume 103, Number 2 (2016), 319-362.

Dates
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1463404121

Digital Object Identifier
doi:10.4310/jdg/1463404121

Mathematical Reviews number (MathSciNet)
MR3504952

Zentralblatt MATH identifier
1351.53013

Citation

Meeks, William H.; Pérez, Joaquín; Ros, Antonio. Local removable singularity theorems for minimal laminations. J. Differential Geom. 103 (2016), no. 2, 319--362. doi:10.4310/jdg/1463404121. https://projecteuclid.org/euclid.jdg/1463404121


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