Minimal surfaces

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.

51p tuanloccuoi 04-01-2013 20 7   Download

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...

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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...

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The theory of polyhedral surfaces and, more generally, the field of discrete differential geometry are presently emerging on the border of differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with a finite number of elements (polyhedra), the theory of polyhedral surfaces aims at a development of discrete equivalents of the geometric notions and methods of surface theory. The latter appears then as a limit of the refinement of the discretization. ...

35p noel_noel 17-01-2013 21 5   Download

The tension structures discussed in this book are predominantly roofing forms created from pre-stressed cable nets, cable trusses, and continuous membranes (fabric structures). A unique feature in their design is form-finding an interactive process of defining the shape of a structure under tension. The book discusses the role of stable minimal surfaces (minimum energy forms occurring in natural objects, such as soap films) in finding optimal shapes of membrane and cable structures.

217p namde04 03-05-2013 38 10   Download

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). ...

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We give a complete topological classification of properly embedded minimal surfaces in Euclidian three-space. 1. Introduction In 1980, Meeks and Yau [15] 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 [6] proved that any two triply periodic minimal surfaces in R3 are properly ambiently isotopic.

21p dontetvui 17-01-2013 25 5   Download

The incremental algorithm introduced in (Dale and Reiter, 1995) for producing distinguishing descriptions does not always generate a minimal description. In this paper, I show that when generalised to sets of individuals and disjunctive properties, this approach might generate unnecessarily long and ambiguous and/or epistemically redundant descriptions.

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These lectures intend to give a self-contained exposure of some techniques for computing the evolution of plane curves. The motions of interest are the so-called motions by curvature. They mean that, at any instant, each point of the curve moves with a normal velocity equal to a function of the curvature at this point. This kind of evolution is of some interest in differential geometry, for instance in the problem of minimal surfaces.

187p camchuong_1 04-12-2012 23 7   Download

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...

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The outer layer had significantly higher SG and bending properties than the inner layer. The SG varied along the culm height. The top portions had consistently higher SG than the base. Bending strength had a strong positive correlation with SG. In order to industrially use bamboo strips efficiently, it is advisable to remove minimal surface material to produce high strength bamboo composites. Compression properties parallel to the longitudinal direction was significantly higher than perpendicular to the longitudinal direction.

79p loixinloi 08-05-2013 22 4   Download

Preconstruction planning should be used to sequence major grading activities to minimize the exposure time of graded or denuded areas. The erosion prevention and sediment control measures and/or plans shall be modified as necessary so that they are effective at all times throughout the course of the project. The Operator will be responsible for the implementation and execution of all storm water runoff controls.

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Optimize your Augmented Category 6 performance at the workstation with ADC’s new six-port surface mount box. An integral part of ADC’s TrueNet® CopperTen™ structured cabling system, its the world’s first Augmented Category 6 structured cabling system to enable 10 Gigabit Ethernet over a full 100 meters of UTP cable. Installed in high-performance networks worldwide, the system’s patent-pending design minimizes alien crosstalk and insertion loss and meets the performance requirements of IEEE 802.3an and TIA 568-B.2-10 draft standards....

2p halanh 14-08-2009 68 2   Download

Several proteins that interact with cell surface glycolipids share a common fold with a solvent-exposed aromatic residue that stacks onto a sugar ring of the glycolipid (CH–pstacking interaction). Stacking interactions between aromatic residues (p–pstacking) also play a pivotal role in the assembly pro-cess, including many cases of amyloid fibril formation.

12p inspiron33 23-03-2013 13 2   Download

For decades, endocytosis has been recognized as a fundamental cellular process that regulates the uptake of small molecules (cell surface proteins, bacteria, toxins, etc.) into the cell. So why, after years of study, does this simple process warrant more discussion? Anyone who has examined the endocytic pathway will appreciate that this conceptually simple mechanism is highly complex and sophisticated. Like ballet dancers who make their synchronous performance seem effortless, the cell brings in molecules via a carefully choreographed mechanism.

0p xunu1311 02-11-2012 22 1   Download

During the anodic etch, a high acid content, low solution temperature, and high current density will minimize smut formation. Carryover of water into the anodic etching solution should be held to a minimum, and long transfer times after the anodic etch should be avoided. Cold rolled steel that has been subjected to deep drawing and certain prepickled hot rolled steels with glazed brownishcolored surfaces may be exceedingly difficult to clean. For these materials, a solution of 25 to 85 vol% nitric acid has proved effective....

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Bhushan, B. “Microscratching/Microwear, Nanofabrication/Nanomachining...” Handbook of Micro/Nanotribology. Ed. Bharat Bhushan Boca Raton: CRC Press LLC, 1999 © 1999 by CRC Press LLC Microscratching/ Microwear, Nanofabrication/ Nanomachining, and Nano/Picoindentation Using Atomic Force Microscopy Bharat Bhushan 7.1 7.2 7.3 7.4 7.5 7.6 Introduction Experimental Techniques AFM for Microscratching/Microwear and Nanoindentation • Nano/Picoindenter 7 Microscratching/Microwear Studies Nanofabrication/Nanomachining Studies Nano/Picoindentation Closure References 7.

22p medinova 26-10-2010 54 8   Download

Wear of sliding surfaces can occur by one or more wear mechanisms, including adhesive, abrasive, fatigue, impact, corrosive, and fretting. The wear rate, a measure of wear, generally needs to be minimized (Bhushan, 1996). As the dimensions of components and loads used continue to decrease (such as in microelectromechanical systems or MEMS), scratching/wear and mechanical properties at the micro- to

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CHAPTER 5 SPECIAL-PURPOSE MECHANISMS NINE DIFFERENT BALL SLIDES FOR LINEAR MOTION Fig. 1 V-grooves and flat surface make a simple horizontal ball slide for reciprocating motion where no side forces are present and a heavy slide is required to keep the balls in continuous contact. The ball cage ensures the proper spacing of the balls and its contacting surfaces are hardened and lapped. Fig. 2 Double V grooves are necessary where the slide is in a vertical position or when transverse loads are present. Screw adjustment or spring force is required to minimize any looseness in the slide.

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Described as a structural/LID hybrid, the Modular Wetland System – Linear is a revolutionary stormwater treatment system. This treatment system utilizes an innovative combination of physically passive and natural biological treatment processes, including the use of a breakthrough filter media, BioMediaGREEN, which acts as a pre-treatment media filter for the enhanced 4th generation sub-surface flow wetland. These features combined with other various treatment and flow control technologies has lead to a system that maximizes pollutant removal and minimizes maintenance. ...

14p tainhacmienphi 19-02-2013 25 4   Download