#### Filter Results:

- Full text PDF available (43)

#### Publication Year

1978

2017

- This year (1)
- Last 5 years (6)
- Last 10 years (20)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

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 de nite lower bound say RicMn i n In Sections and sometimes in we also assume a lower volume bound Vol B pi v In this case the sequence is said to be non collapsing… (More)

This paper is the second in a series where we attempt to give a complete description of the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R. We… (More)

In this note we prove some bounds for the extinction time for the Ricci flow on certain 3-manifolds. Our interest in this comes from a question that Grisha Perelman asked the first author at a dinner in New York City on April 25th of 2003. His question was “what happens to the Ricci flow on the 3-sphere when one starts with an arbitrary metric? In… (More)

This paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 (with the flat metric).… (More)

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 nonsimply connected embedded minimal surfaces of any given fixed genus. The first of these asserts that any such surface without small necks can be obtained by gluing together two… (More)

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 R. This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see [CM15] for discussion of… (More)

Twenty years ago Yau, 56], generalized the classical Liouville theorem of complex analysis to open manifolds with nonnegative Ricci curvature. Speciically, he proved that a positive harmonic function on such a manifold must be constant. This theorem of Yau was considerably generalized by Cheng-Yau (see 15]) by means of a gradient estimate which implies the… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in… (More)

In this paper we will prove the Calabi-Yau conjectures for embedded surfaces (i.e., surfaces without self-intersection). In fact, we will prove considerably more. The heart of our argument is very general and should apply to a variety of situations, as will be more apparent once we describe the main steps of the proof later in the introduction. The… (More)

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 (in fact, Corollary III.3.5 below is used in [CM5]). To describe general planar domains (in… (More)