论文标题
Loewner方程中的驾驶员，打击时间和焊接
Drivers, hitting times, and weldings in Loewner's equation
论文作者
论文摘要
除了保形焊接$φ$外，简单曲线$γ$在上半平面生长的驾驶功能$ξ$，并通过Loewner的微分方程达到$τ$。虽然已仔细检查了Loewner Transform $γ\ mapstoξ$及其逆$ξ\mapstoγ$，但对地图$ξ\ mapstoτ\ mapstoφ$的关注减少了。我们研究了它们的连续性特性，并表明均匀的驱动器收敛意味着即使相应的曲线不收敛，均匀的打击时间收敛和均匀的焊接收敛。焊接收敛既不意味着撞击时间也不意味着驱动器收敛，而击打时间收敛则意味着（至少）恒定驱动器的情况中的驱动器收敛。 作为应用程序，我们表明，有限loewner能量的曲线$γ$可以通过与$γ$的焊接相匹配的能量最小化器可以很好地近似。
In addition to conformal weldings $φ$, simple curves $γ$ growing in the upper half plane generate driving functions $ξ$ and hitting times $τ$ through Loewner's differential equation. While the Loewner transform $γ\mapsto ξ$ and its inverse $ξ\mapsto γ$ have been carefully examined, less attention has been paid to the maps $ξ\mapsto τ\mapsto φ$. We study their continuity properties and show that uniform driver convergence implies uniform hitting time convergence and uniform welding convergence, even when the corresponding curves do not converge. Welding convergence implies neither hitting time nor driver convergence, while hitting time convergence implies driver convergence in (at least) the case of constant drivers. As an application, we show that a curve $γ$ of finite Loewner energy can be well approximated by an energy minimizer that matches $γ$'s welding on a sufficiently-fine mesh.
