Regularity of discs attached to a submanifold ofC n

Letp be an analytic disc attached to a generating CR-submanifoldM of C ⁿ . It is proved that some recently introduced conditions onp andM which imply that the family of all smallC ^α holomorphic perturbations ofp alongM is a Banach submanifold of (A^α(D))ⁿ are equivalent. These conditions are given in terms of the partial indices of the discp attached toM and “holomorphic sections” of the conormal bundle ofM along p(∂D). Also, a sufficient geometric conditionon p andM is given so that the family of all smallC ^α holomorphic perturbationsof p alongM, fixed at some boundary point, is a Banach submanifold of (A ^α (D))ⁿ.     

Analytic Discs Attached From the Outside Have Knotted Boundaries

Let be a pseudoconvex domain in C² with smooth boundary, andlet be a smooth embedded analytic disc intersecting transversally along the curve A. Then A isknotted in . 2000 Mathematics Subject Classification 32U99.     

Generalized Ahlfors functions

Let be a bordered Riemann surface with genus and boundary components. Let be a smooth family of smooth Jordan curves in which all contain the point 0 in their interior. Let and let be the family of all bounded holomorphic functions on such that and for almost every . Then there exists a smooth up to the boundary holomorphic function with at most zeros on so that for every and such that for every . If, in addition, all the curves are strictly convex, then is unique among all the functions from the family .

     

Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3

We report the THz response of thin films of the topological insulator Bi2Se3. At low frequencies, transport is essentially thickness independent showing the dominant contribution of the surface electrons. Despite their extended exposure to ambient conditions, these surfaces exhibit robust properties including narrow, almost thickness-independent Drude peaks, and an unprecedentedly large polarization rotation of linearly polarized light reflected in an applied magnetic field. This Kerr rotation can be as large as 65° and can be explained by a cyclotron resonance effect of the surface states.     

Infrared hall effect in high- T(c) superconductors: evidence for non-fermi-liquid hall scattering

Infrared ( 20-120 and 900-1100 cm(-1)) Faraday rotation and circular dichroism are measured in high- T(c) superconductors using sensitive polarization modulation techniques. Optimally doped YBa2Cu3O7 thin films are studied at temperatures in the range ( 15相似文献