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- W4231522162 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, $f(1) = p$, $fâ (1) = v$ if $partial D in {C^k}$, $k geqslant 14$). Consequently, we can foliate $overline D$ with these extremal analytic discs." @default.
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- W4231522162 date "1988-11-01" @default.
- W4231522162 modified "2023-10-18" @default.
- W4231522162 title "Extremal Analytic Discs With Prescribed Boundary Data" @default.
- W4231522162 doi "https://doi.org/10.2307/2001127" @default.
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