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Search: MSC category 30F99 ( None of the above, but in this section )

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1. CMB 2016 (vol 59 pp. 776)

Gauthier, Paul M; Sharifi, Fatemeh
 The CarathÃ©odory Reflection Principle and Osgood-CarathÃ©odory Theorem on Riemann Surfaces The Osgood-CarathÃ©odory theorem asserts that conformal mappings between Jordan domains extend to homeomorphisms between their closures. For multiply-connected domains on Riemann surfaces, similar results can be reduced to the simply-connected case, but we find it simpler to deduce such results using a direct analogue of the CarathÃ©odory reflection principle. Keywords:bordered Riemann surface, reflection principle, Osgood-CarathÃ©odoryCategories:30C25, 30F99

2. CMB Online first

Gauthier, Paul M; Sharifi, Fatemeh
 Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces It is known that if $E$ is a closed subset of an open Riemann surface $R$ and $f$ is a holomorphic function on a neighbourhood of $E,$ then it is usually" not possible to approximate $f$ uniformly by functions holomorphic on all of $R.$ We show, however, that for every open Riemann surface $R$ and every closed subset $E\subset R,$ there is closed subset $F\subset E,$ which approximates $E$ extremely well, such that every function holomorphic on $F$ can be approximated much better than uniformly by functions holomorphic on $R$. Keywords:Carleman approximation, tangential approximation, Myrberg surfaceCategories:30E15, 30F99

3. CMB 2000 (vol 43 pp. 183)

Ionesei, Gheorghe
 A Gauge Theoretic Proof of the Abel-Jacobi Theorem We present a new, simple proof of the classical Abel-Jacobi theorem using some elementary gauge theoretic arguments. Keywords:Abel-Jacobi theorem, abelian gauge theoryCategories:58D27, 30F99
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