Given a compact closed subset M of a line segment in R, we construct a sequence of minimal surfaces Σk embedded in a neighborhood C of the line segment that converge smoothly to a limit lamination of C away from M . Moreover, the curvature of this sequence blows up precisely on M , and the limit lamination has non-removable singularities precisely on the boundary of M .

We show how an incompressible Seifert surface F for a knot K in S can be used to create an essential lamination LF in the complement of each of an in nite class of knots associated to F . This lamination is persistent for these knots; it remains essential under all non-trivial Dehn llings of the knot complement. This implies a very strong form of Property P for each of these knots.

A geodesic lamination L on a closed hyperbolic surface S, when provided with a transverse measure μ, gives rise to a “dual R-tree” Tμ, together with an action of G = π1S on Tμ by isometries. A point of Tμ corresponds precisely to a leaf of the lift L̃ of L to the universal covering S̃ of S, or to a complementary component of L̃ in S̃. The G-action on T is induced by the G-action on S̃ as deck transf...

PURPOSE Abnormal retinal angiogenesis leads to visual impairment and blindness. Understanding how retinal vessels develop normally has dramatically improved treatments for people with retinal vasculopathies, but additional information about development is required. Abnormal neuron patterning in the outer retina has been shown to result in abnormal vessel development and blindness, for example, ...

We give a complete proof of the Bers-Sullivan-Thurston Density Conjecture. In the light of the Ending lamination theorem, it suffices to prove that any collection of possible ending invariants is realized by some algebraic limit of geometrically finite hyperbolic manifolds. The ending invariants are either Riemann surfaces or filling laminations supporting Masur domain measured laminations and ...

We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric [Br2], these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and...

A mechanism amenable to laminate and fold flows is identified and quantified. This laminating mechanism follows from a physical and experimental approach relying on the interlaced structure of velocity and Lagrangian acceleration. The Lagrangian acceleration being the resultant of the forces applied on particle fluids, the component of acceleration perpendicular to the velocity vector allows th...

We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric [Br2], these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and...

Although the manufacture of rolls is in constant improvement, the requirements for superior quality rolls have not yet been completely satisfied, in many cases the absence of quality rolls preventing the realization of quality laminates or of productivity of which rolling mills are capable. In the selection of materials several factors have to be considered including the type of rolling mill, t...

In the retina, like in most other brain regions, developing neurons are arranged into distinct layers giving the mature tissue its stratified appearance. This process needs to be highly controlled and orchestrated, as neuronal layering defects lead to impaired retinal function. To achieve successful neuronal layering and lamination in the retina and beyond, three main developmental steps need t...