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.
A Fourier restriction estimate for surfaces of positive curvature in $\mathbb{R}^6$
