We construct smooth irreducible curves of the lowest possible degrees in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded into those surfaces. Moreover we characterize line bundles on quadric and cubic surfaces such that the complete linear systems of the line bundles have a smooth irreducible curve whose complement is Kobayashi hyperbolically imbedded.

The inverse source problem for a monochromatic source imbedded in a nonabsorbing inhomogeneous medium is investigated within the framework of the reduced scalar wave equation. The Porter-Bojarski integral equation previously formulated for sources imbedded in vacuum is generalized to this case, as are the class of nonradiating and minimum-energy sources considered in Part I [J. Opt. Soc. Am. 72...

We construct examples of potentials V (x) satisfying |V (x)| ≤ h(x) 1+x , where the function h(x) is growing arbitrarily slowly, such that the corresponding Schrödinger operator has imbedded singular continuous spectrum. This solves one of the fifteen “twenty-first century” problems for Schrödinger operators posed by Barry Simon in [22]. The construction also provides the first example of a Sch...

The purpose of this note is to state a collection of results, all related to questions of uniqueness of smooth neighborhoods of finite complexes as imbedded (nicely) in differentiable manifolds. The reported results will appear in subsequent papers, the first of which is [l ]. The approach taken is always via the theory of simple homotopy types (due to J. H. C. Whitehead), and the main theorem ...