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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Extremal analytic discs with prescribed boundary data
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by Chin-Huei Chang, M. C. Hu and Hsuan-Pei Lee
Trans. Amer. Math. Soc. 310 (1988), 355-369
DOI: https://doi.org/10.1090/S0002-9947-1988-0930081-7

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.
References
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 310 (1988), 355-369
  • MSC: Primary 32H15; Secondary 32D15, 32H20
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0930081-7
  • MathSciNet review: 930081