论文标题
$ \ mathbb {d}^3 $中三分挑选问题的独特品种的几何形状
Geometry of uniqueness varieties for a three-point Pick problem in $\mathbb{D}^3$
论文作者
论文摘要
Motivated by the recent progress of research on extending holomorphic functions defined on subvarieties of classical domains and its connections to the 3-point Pick interpolation, we study a special class of two-dimensional algebraic subvarieties $M_α$ of the unit tridisc, defined as the sets $$\lbrace (z_1,z_2,z_3)\in \ Mathbb {d}^3：α_1Z_1+α_2Z_2+α_3Z_3= \overlineα_1Z_2Z_3+\overlineα_2Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_1Z_3Z_3Z_1Z_1Z_1Z_2\ rbrace \ rbrace。 $α$，因此$m_α$看起来是其独特性的变化。我们还描述了$M_α$的几种几何特性，并显示了任意两个表面$M_α$和$M_β$之间的生物形态等效性，其中三元$α$和$β$满足所谓的三角形不等式。
Motivated by the recent progress of research on extending holomorphic functions defined on subvarieties of classical domains and its connections to the 3-point Pick interpolation, we study a special class of two-dimensional algebraic subvarieties $M_α$ of the unit tridisc, defined as the sets $$\lbrace (z_1,z_2,z_3)\in \mathbb{D}^3:α_1z_1+α_2z_2+α_3z_3=\overlineα_1z_2z_3+\overlineα_2z_1z_3+\overlineα_3z_1z_2\rbrace.$$ In this paper we show that given non-degenerated extremal maximal $3$-point Pick problem there exists an $α$ such that $M_α$ appears as its uniqueness variety. We also describe several geometric properties of $M_α$ and show the biholomorphic equivalence between any two surfaces $M_α$ and $M_β$, where the triples $α$ and $β$ satisfy the so called triangle inequality.
