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The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected
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abstract
This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key is to understand the structure of an embedded minimal disk in a ball in $\RR^3$. This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see [CM15] for discussion of the local case and [CM13], [CM14] where we have surveyed our results about embedded minimal disks.
Forward citations
Cited by 2 Pith papers
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Calabi-Yau Conjecture for Minimal Hypersurfaces in $\mathbb{R}^4$ with bounded geometry
Complete embedded minimal hypersurfaces in R^4 with bounded second fundamental form and finite second Betti number are proper.
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Half-Space Theorem for Minimal Hypersurfaces in $\mathbb{R}^4$
Complete properly embedded minimal hypersurfaces Σ³≅R³ in R⁴ with bounded curvature that lie in a slab (or half-space with cubic growth) are hyperplanes.
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