Remarks on the Alexander-wermer Theorem for Curves
نویسندگان
چکیده
We give a new proof of the Alexander-Wermer Theorem that characterizes the oriented curves in C which bound positive holomorphic chains, in terms of the linking numbers of the curve with algebraic cycles in the complement. In fact we establish a slightly stronger version which applies to a wider class of boundary 1-cycles. Arguments here are based on the Hahn-Banach Theorem and some geometric measure theory. Several ingredients in the original proof have been eliminated.
منابع مشابه
O ct 2 00 6 REMARKS ON THE ALEXANDER - WERMER THEOREM FOR CURVES
We give a new proof of the Alexander-Wermer Theorem that characterizes the oriented curves in C n which bound positive holomorphic chains, in terms of the linking numbers of the curve with algebraic cycles in the complement. In fact we establish a slightly stronger version which applies to a wider class of boundary 1-cycles. Arguments here are based on the Hahn-Banach Theorem and some geometric...
متن کاملRemarks on the Paper ``Coupled Fixed Point Theorems for Single-Valued Operators in b-Metric Spaces''
In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...
متن کاملUniform Algebras on Curves
The proofs use the notion of analytic structure in a maximal ideal space. J. Wermer first obtained results along these lines and further contributions were made by E. Bishop and H. Royden and then by G. Stolzenberg [5] who proved STOLZENBERG'S THEOREM. Let XQC be a polynomially convex set. Let KQC be a finite union of Q-curves. Then (XKJK)*—X\JK is a {possibly empty) pure 1-dimensional analytic...
متن کاملComplex Interpolation of R-norms, Duality and Foliations
The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our result...
متن کاملOn the $c_{0}$-solvability of a class of infinite systems of functional-integral equations
In this paper, an existence result for a class of infinite systems of functional-integral equations in the Banach sequence space $c_{0}$ is established via the well-known Schauder fixed-point theorem together with a criterion of compactness in the space $c_{0}$. Furthermore, we include some remarks to show the vastity of the class of infinite systems which can be covered by our result. The a...
متن کامل