Boundary cross theorem in dimension 1

Peter Pflug; Viet-Anh Nguyen

Boundary cross theorem in dimension 1

复变函数 2007-05-23 v3

作者: Peter Pflug , Viet-Anh Nguyen

摘要

Let $X, Y$ be two complex manifolds of dimension 1 which are countable at infinity, let $D\subset X,$ $G\subset Y$ be two open sets, let $A$ (resp. $B$ ) be a subset of $\partial D$ (resp. $\partial G$ ), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Suppose in addition that $D$ (resp. $G$ ) is {\it Jordan-curve-like on $A$ } (resp. $B$ ) and that $A$ and $B$ are {\it of positive length}. We determine the "envelope of holomorphy" $\hat{W}$ of $W$ in the sense that any function locally bounded on $W,$ measurable on $A\times B,$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a function holomorphic on the interior of $\hat{W}.$

关键词

holomorphic mappings holomorphic dynamics algebraic topology

引用

@article{arxiv.math/0503326,
  title  = {Boundary cross theorem in dimension 1},
  author = {Peter Pflug and Viet-Anh Nguyen},
  journal= {arXiv preprint arXiv:math/0503326},
  year   = {2007}
}

备注

43 pages, to appear in "Annales Polonici Mathematici". This is the revised version of our article put on Arxiv in March 2005

Boundary cross theorem in dimension 1

摘要

关键词

引用

备注

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