On Complete Open Manifolds of Positive Curvature

1969 ◽  
Vol 90 (1) ◽  
pp. 75 ◽  
Author(s):  
Detlef Gromoll ◽  
Wolfgang Meyer
Keyword(s):  
Positive Curvature ◽  
Open Manifolds

scholarly journals Martin points on open manifolds of non-positive curvature

2007 ◽  
Vol 359 (12) ◽  
pp. 5697-5724 ◽  
Author(s):  
Jianguo Cao ◽  
Huijun Fan ◽  
François Ledrappier
Keyword(s):  
Positive Curvature ◽  
Open Manifolds

Biophysics (and sociology) of ceramides.

2005 ◽  
Vol 72 ◽  
pp. 177-188 ◽  
Author(s):  
Félix M. Goñi ◽  
F-Xabier Contreras ◽  
L-Ruth Montes ◽  
Jesús Sot ◽  
Alicia Alonso
Keyword(s):  
Cell Biology ◽  
Positive Curvature ◽  
Acyl Chain ◽  
Cell Signalling ◽  
Hexagonal Structure ◽  
Lipid Monolayer ◽  
Flip Flop ◽  
Long Chain ◽  
Bilayer Permeability

In the past decade, the long-neglected ceramides (N-acylsphingosines) have become one of the most attractive lipid molecules in molecular cell biology, because of their involvement in essential structures (stratum corneum) and processes (cell signalling). Most natural ceramides have a long (16-24 C atoms) N-acyl chain, but short N-acyl chain ceramides (two to six C atoms) also exist in Nature, apart from being extensively used in experimentation, because they can be dispersed easily in water. Long-chain ceramides are among the most hydrophobic molecules in Nature, they are totally insoluble in water and they hardly mix with phospholipids in membranes, giving rise to ceramide-enriched domains. In situ enzymic generation, or external addition, of long-chain ceramides in membranes has at least three important effects: (i) the lipid monolayer tendency to adopt a negative curvature, e.g. through a transition to an inverted hexagonal structure, is increased, (ii) bilayer permeability to aqueous solutes is notoriously enhanced, and (iii) transbilayer (flip-flop) lipid motion is promoted. Short-chain ceramides mix much better with phospholipids, promote a positive curvature in lipid monolayers, and their capacities to increase bilayer permeability or transbilayer motion are very low or non-existent.

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

Imbedding open manifolds in compact ones

1978 ◽  
Vol 19 (2) ◽  
pp. 197-211 ◽  
Author(s):  
A. Z. Dymov
Keyword(s):  
Open Manifolds

scholarly journals Embeddings of open manifolds

1999 ◽  
Vol 351 (6) ◽  
pp. 2353-2373
Author(s):  
Nancy Cardim
Keyword(s):  
Open Manifolds

The entrainment interface

1972 ◽  
Vol 51 (1) ◽  
pp. 97-118 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Surface Area ◽  
Large Scale ◽  
Positive Curvature ◽  
Lagrangian Description ◽  
Eulerian Description ◽  
Entrainment Process ◽  
Necessary And Sufficient ◽  
Small Disturbances

A theory is developed to describe the evolution of the entrainment interface in turbulent flow, in which the surface is convoluted by the large-scale eddies of the motion and at the same time advances relative to the fluid as a result of the micro-scale entrainment process. A pseudo-Lagrangian description of the process indicates that the interface is characterized by the appearance of ‘billows’ of negative curvature, over which surface area is, on average, being generated, separated by re-entrant wedges (lines of very large positive curvature) where surface area is consumed. An alternative Eulerian description allows calculation of the development of the interfacial configuration when the velocity field is prescribed. Several examples are considered in which the prescribed velocity field in the z direction is of the general form w = Wf(x – Ut), where the maximum value of the function f is unity. These indicate the importance of leading points on the surface which are such that small disturbances in the vicinity will move away from the point in all directions. The necessary and sufficient condition for the existence of one or more leading points on the surface is that U [les ] V, the speed of advance of an element of the surface relative to the fluid element at the same point. The existence of leading points is accompanied by the appearance of line discontinuities in the surface slope re-entrant wedges, In these circumstances, the overall speed of advance of the convoluted surface is found to be W + (V2 – U2)½, where W is the maximum outwards velocity in the region; this result is independent of the distribution f.When the speed U with which an ‘eddy’ moves relative to the outside fluid is greater than the speed of advance V of an element of the front, the interface develops neither leading points nor discontinuities in slope; the amplitude of the surface convolutions and the overall entrainment speed are both reduced greatly. In a turbulent flow, therefore, the large-scale motions influencing entrainment are primarily those that move slowly relative to the outside fluid (with relative speed less than V). The experimental results of Kovasznay, Kibens & Blackwelder (1970) are reviewed in the light of these conclusions. It appears that in their experiments the entrainment speed V is of the order fifteen times the Kolmogorov velocity, the large constant of proportionality being apparently the result of augmentation by micro-convolutions of the interface associated with small and meso-scale eddies of the turbulence.

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