Rigidity of circle domains whose boundary hasσ-finite linear measure

Summary Let be a circle domain in the Riemann sphere whose boundary has -finite linear measure. We show that is rigid in the sense that any conformal homeomorphism of onto any other circle domain is equal to the restriction of a Möbius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle, domains whose boundary is a Cantor set of (Hausdorff) dimension one.Oblatum 19-VI-1992 & 2-IV-1993Supported by NSF and Sloan Foundation     

NLS-tupe equations in 2+1 dimensions: New type of solutions and non-isospectral problems

Integrable systems of NLS type in 2+1 dimensions are studied in three ways: their special solutions by Lie point symmetries, breaking-solutions by the ISM, as well as the non-isospectral problems.Department of Mathematics, Statistics and Computing Science, University of New England, Armidale N.S.W. 2351, Australia. E-mail: zhuhan@neumann.une.edu.au, xhe@metz.une.edu.au Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 382–389, June, 1994.     

The projection method for computing multidimensional absolutely continuous invariant measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC ² expanding mappingS: on a bounded region R ^N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm.