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Generic mean curvature flow I; generic singularities
It has long been conjectured that starting at a generic smooth closed embedded surface in R^3, the mean curvature flow remains smooth until it arrives at a singularity in a neighborhood of which theExpand
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On the structure of spaces with Ricci curvature bounded below. II
In this paper and in we study the structure of spaces Y which are pointed Gromov Hausdor limits of sequences f M i pi g of complete connected Riemannian manifolds whose Ricci curvatures have a deExpand
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Ricci curvature and volume convergence
The purpose of this paper is to give a new (integral) estimate of distances and angles on manifolds with a given lower Ricci curvature bound. This will provide us with an integral version of theExpand
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The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected
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 3manifold. The key is to understand the structure ofExpand
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A Course in Minimal Surfaces
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differentialExpand
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The Calabi-Yau conjectures for embedded surfaces
In this talk I will discuss the proof of the Calabi-Yau conjectures for embedded surfaces. This is joint work with Bill Minicozzi, [CM9]. The Calabi-Yau conjectures about surfaces date back to theExpand
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Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
We prove a new estimate on manifolds with a lower Ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a Holder continuous way along theExpand
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The min--max construction of minimal surfaces
In this paper we survey with complete proofs some well-known, but hard to find, results about constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min-max arguments.Expand
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The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus
This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for \itnonsimply connected embeddedExpand
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