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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Extremal analytic discs with prescribed boundary data


Authors: Chin-Huei Chang, M. C. Hu and Hsuan-Pei Lee
Journal: Trans. Amer. Math. Soc. 310 (1988), 355-369
MSC: Primary 32H15; Secondary 32D15, 32H20
MathSciNet review: 930081
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Abstract: This paper concerns the existence and uniqueness of extremal analytic discs with prescribed boundary data in a bounded strictly linearly convex domain $ D$ in $ {{\mathbf{C}}^n}$. We prove that for any two distinct points $ p$, $ q$ in $ \partial D$ (respectively, $ p \in \partial D$ and a vector $ v$ such that $ \sqrt { - 1} v \in {T_p}(\partial D)$ and $ \langle v,\,\overline \nu (p)\rangle = \sum\nolimits_1^n {{v_j}{{\overline \nu }_j}(p) > 0} $ where $ \nu (p)$ is the outward normal to $ \partial D$ at $ p$) there exists an extremal analytic disc $ f$ passing through $ p$, $ q$ if $ \partial D \in {C^k}$, $ k \geqslant 3$ (respectively, $ f(1) = p$, $ f' (1) = v$ if $ \partial D \in {C^k}$, $ k \geqslant 14$). Consequently, we can foliate $ \overline D $ with these extremal analytic discs.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0930081-7
Article copyright: © Copyright 1988 American Mathematical Society