随机平面演化中边界行为的光滑化
Smoothing of Boundary Behaviour in Stochastic Planar Evolutions
摘要：
受Schramm-Loewner发展的迹研究的启发，我们考虑了定义在上半平面$\mathbb{H}$上的全纯向量场$F$的常微分方程所支配的平面区域的发展.我们显示了相关的共形映射的边界行为上的噪声的存在下的平滑效果。更准确地说，如果$F$是Hölder，我们证明了不断变化的域在一致的拓扑结构和它们的边界是连续可微的约旦弧。这与来自确定性设置的示例形成对比，在确定性设置中，域$F(\mathbb{H})$的边界上的角点可以引起对应的演进域的边界上的角点。
英文摘要：
Motivated by the study of trace for Schramm-Loewner evolutions, we consider evolutions of planar domains governed by ordinary differential equations with holomorphic vector fields $F$ defined on the upper half plane $\mathbb{H}$. We show a smoothing effect of the presence of noise on the boundary behaviour of associated conformal maps. More precisely, if $F$ is Hölder, we show that evolving domains vary continuously in uniform topology and their boundaries are continuously differentiable Jordan arcs. This is in contrast with examples from deterministic setting where the corner points on the boundary of domain $F(\mathbb{H})$ may give rise to corner points on the boundaries of corresponding evolving domains.
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。
