相关论文: Embedded minimal disks

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…

We construct a sequence of embedded minimal disks in a ball where the curvatures blow up only at the center. The sequence converges to a limit which is not smooth and not proper.

This paper is the first 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 Riemannian 3-manifold. The key for understanding such…

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…

I briefly review recent developments in the study of circumstellar debris disks, particularly at infrared and sub-millimeter wavelengths, and discuss possible avenues of research for the near future.

We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a…

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. This includes results of J. Pitts, F.…

In this note we propose a min-max theory for embedded hypersurfaces with a fixed boundary and apply it to prove several theorems about the existence of embedded minimal hypersurfaces with a given boundary. A simpler variant of these…

This is a survey of results in the enumeration of lattice paths.

The study of embedded minimal surfaces in $\RR^3$ is a classical problem, dating to the mid 1700's, and many people have made key contributions. We will survey a few recent advances, focusing on joint work with Tobias H. Colding of MIT and…

Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In…

The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.

As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…

We show that an embedded minimal disk in R^3 with large curvature is bilipschitz with a piece of a helicoid. Additionally, a simplified proof of the uniqueness of the helicoid is provided.

We give a generalization of Meeks-Yau's celebrated embeddedness result for the solutions of the Plateau problem for extreme curves.

In this paper we prove that a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface $\overline{M}$ with boundary punctured in a finite…

A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…

In this paper we give two examples of sequences of embedded minimal planar domains in $\mathbb{R}^3$ which converge to singular laminations of $\mathbb{R}^3$. In contrast with the situation for embedded minimal disks, these examples do not…

This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as…

This is a brief review of spin physics in semiconductors, as well as of the historic roots of the recent very active research of spin-related phenomena. The perspectives of "spintronics" are also discussed.