The $$L^p$$-Calderón–Zygmund inequality on non-compact manifolds of positive curvature

The structure of local and global harmonic morphisms between Riemannian manifolds, with totally fibres, is investigated. It is shown that non-positive curvature of the domain obstructs the existence of global harmonic morphisms with totally geodesic fibres and the only such maps from compact Riemannian manifolds of non-positive curvature are, up to a homothety, totally geodesic Riemannian submersions. Similar results are obtained for local harmonic morphisms with totally geodesic fibres from open subsets of non-negatively curved compact and non-compact manifolds. During the course, we prove non-existence of submersive harmonic morphisms with totally geodesic fibres from some important domains, for instance from compact locally symmetric spaces of non-compact type and open subsets of symmetric spaces of compact type.

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Biophysics (and sociology) of ceramides.

Biochemical Society Symposium ◽

10.1042/bss0720177 ◽

2005 ◽

Vol 72 ◽

pp. 177-188 ◽

Cited By ~ 28

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.

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