Annals of Mathematics
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. Although the focus of this paper, general planar domains, is more in line with [CM6], we will prove a result here (namely, Corollary III.
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). This study is undertaken here and completed in [CM6]. These local results are then applied in [CM7] where we describe the general structure of ﬁxed genus surfaces in 3-manifolds. There are two local models for...
The space of embedded minimal surfaces of ﬁxed genus in a 3-manifold II; Multi-valued graphs in disks
By Tobias H. Colding and William P. Minicozzi II*
0. Introduction This paper is the second in a series where we give a 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 R3 . We show here that if the curvature of such a disk...
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 of an embedded minimal disk in a ball in R3 . This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see the discussion around Figure 12 for the local case and [CM15] for some more details. Our main results are Theorem 0.1 (the lamination theorem) and Theorem 0.2 (the one-sided curvature estimate). ...
We give a complete topological classiﬁcation of properly embedded minimal surfaces in Euclidian three-space. 1. Introduction In 1980, Meeks and Yau  proved that properly embedded minimal surfaces of ﬁnite topology in R3 are unknotted in the sense that any two such homeomorphic surfaces are properly ambiently isotopic. Later Frohman  proved that any two triply periodic minimal surfaces in R3 are properly ambiently isotopic.
In this paper we will discuss the geometry of ﬁnite topology properly embedded minimal surfaces M in R3 . M of ﬁnite topology means M is homeomorphic to a compact surface M (of genus k and empty boundary) minus a ﬁnite number of points p1 , ..., pj ∈ M , called the punctures. A closed neighborhood E of a puncture in M is called an end of M . We will choose the ends suﬃciently small so they are topologically S 1 × [0, 1) and hence, annular. We remark that M is orientable since M is properly...
The carbon dioxide molecule becomes cluster to
minimize the free energy; as a result pore nucleation is created. These pores cause the
significant expansion of polymeric volume and decrease in polymeric density. A three-
dimensional porous structure (scaffolds) is formed after completion of foaming process.
The porosity of the scaffolds is controlled by the use of porogens like sugar, salts and wax
Main Receive Aperture and Analog Beamforming Data to be Processed The Processing Needs and Major Issues Temporal DOF Reduction Adaptive Filtering with Needed and Sample-Supportable DOF and Embedded CFAR Processing 70.6 Scan-To-Scan Track-Before-Detect Processing 70.7 Real-Time Nonhomogeneity Detection and Sample Conditioning and Selection 70.8 Space or Space-Range Adaptive Pre-Suppression of Jammers 70.9 A STAP Example with a Revisit to Analog Beamforming 70.
EURASIP Journal on Applied Signal Processing 2003:6, 514–529 c 2003 Hindawi Publishing Corporation
Memory-Optimized Software Synthesis from Dataﬂow Program Graphs with Large Size Data Samples
The School of Electrical Engineering and Computer Science, Seoul National University, Seoul 151-742, Korea Email: email@example.com
The School of Electrical Engineering and Computer Science, Seoul National University, Seoul 151-742, Korea Email: firstname.lastname@example.org.
(BQ) Machining speed and surface integrity continue to be issues of focus in current wire EDM research. In this light, the proof-of-concept of a hybrid wire EDM process that utilizes a wire embedded with electrically non-conducting abrasives is presented. Material removal in this novel process is realized through electrical erosion that is augmented by two-body abrasion. This is shown to bring about a significant improvement in the removal rate and generate surfaces with minimal recast material, in comparison to an equivalent wire EDM process.