退化CR奇点附近的局部多项式壳-- Bishop圆再探
The local polynomial hull near a degenerate CR singularity -- Bishop discs revisited
摘要：
设S是C^2中的光滑实曲面，p \in S是一点，在该点处的切面是一条复直线。如何确定S是否局部多项式凸在这样一个p -即在CR奇点？即使当T_p（S）与S在p处的接触阶数等于2时，也不存在清晰的特征;抛物点造成了困难。因此，我们研究非抛物CR奇点。我们表明，存在或不存在的主教光盘周围的某些非抛物CR奇点是完全由马斯洛夫型指数。这一结果包含了所有已知的事实主教光盘周围的订单二，非抛物CR奇点。在与T_p（S）有高阶接触的CR奇点上，Bishop圆的充分条件已被研究过.这些结果依赖于一个亚谐性条件，在许多简单的情况下失败。因此，我们超越了位势论，并提炼了某些可以追溯到毕晓普的思想。
英文摘要：
Let S be a smooth real surface in C^2 and let p\in S be a point at which the tangent plane is a complex line. How does one determine whether or not S is locally polynomially convex at such a p --- i.e. at a CR singularity ? Even when the order of contact of T_p(S) with S at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study non-parabolic CR singularities. We show that the presence or absence of Bishop discs around certain non-parabolic CR singularities is completely determined by a Maslov-type index. This result subsumes all known facts about Bishop discs around order-two, non-parabolic CR singularities. Sufficient conditions for Bishop discs have earlier been investigated at CR singularities having high order of contact with T_p(S). These results relied upon a subharmonicity condition, which fails in many simple cases. Hence, we look beyond potential theory and refine certain ideas going back to Bishop.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
