有理逼近与拉格朗日包含
Rational approximation and Lagrangian inclusions
摘要：
证明了具有双横截自交点和标准开Whitney伞的$\mathbb C^2$中的拉格朗日包含是有理凸的。作为应用，我们证明了除$S^2$和$\mathbb RP_2$外，任何紧致曲面$S$都存在一对光滑复值函数$f_1$，$f_2$，且$S$上的任何连续复值函数都是$R_j(f_1,f_2)$序列的一致极限，其中$R_j(z_1,z_2)$是$\mathbb C^2$中的有理函数.
英文摘要：
We show that a Lagrangian inclusion in $\mathbb C^2$ with double transverse self-intersection points and standard open Whitney umbrellas is rationally convex. As an application we show that any compact surface $S$, except $S^2$ and $\mathbb RP_2$, admits a pair of smooth complex-valued functions $f_1$, $f_2$ with the property that any continuous complex valued function on $S$ is a uniform limit of a sequence of $R_j(f_1,f_2)$, where $R_j(z_1,z_2)$ are rational functions in $\mathbb C^2$.
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