论文标题
在表面上的全体形态叶子的限制集补充的凸面
Convexity of complements of limit sets for holomorphic foliations on surfaces
论文作者
论文摘要
令$ \ Mathcal f $为紧凑的Káhler表面上具有双曲线奇异性和没有叶状周期的圆形叶状。我们证明，如果$ \ Mathcal F $的限制集的lebesgue度量为零，则其补充是对Stein域的修改。该证明是在几个步骤中建造一个正常捆绑包$ \ MATHCAL F $的正曲率的度量。然后，我们通过将Brunella的想法适应我们的奇异背景来构建适当的严格多元性耗尽功能，以构建限制集的补充功能。当限制集很薄时，该论点更加普遍，这是依赖布朗尼运动的属性。
Let $\mathcal F$ be a holomorphic foliation on a compact Káhler surface with hyperbolic singularities and no foliation cycle. We prove that if the limit set of $\mathcal F$ has zero Lebesgue measure, then its complement is a modification of a Stein domain. The proof consists in building, in several steps, a metric of positive curvature for the normal bundle of $\mathcal F$ near the limit set. Then we construct a proper strictly plurisubharmonic exhaustion function for the complement of the limit set, by adapting Brunella's ideas to our singular context. The arguments hold more generally when the limit set is thin, a property relying on Brownian motion.
