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The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains

Tobias H. Colding·William P. Minicozzi II
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Abstract

This paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. In [CM3]-[CM5] we describe the case where the surfaces are topologically disks on any fixed small scale. To describe general planar domains (in [CM6]) we need in addition to the results of [CM3]-[CM5] a key estimate for embedded stable annuli which is the main result of this paper. This estimate asserts that such an annulus is a graph away from its boundary if it has only one interior boundary component and if this component lies in a small (extrinsic) ball.

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Tobias H. Colding, William P. Minicozzi II. 2002-10-09. The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains. https://arxiv.org/abs/math/0210141

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