一类复驱动Loewner壳的相变
Phase Transition for a Family of Complex-driven Loewner Hulls
摘要：
在H. Tran对复值驱动函数生成的Loewner壳的研究表明了相变的存在，我们回答了复驱动壳的相变是否与实驱动壳的相变相匹配的问题。这是通过详细研究由$c \in \mathbb{C}$和$τ\geq 0$的驱动函数$c\sqrt{1-t}$和$c\sqrt{τ+ t}$生成的Loewner船体来实现的。此族还提供了新几何行为的示例，这些行为可能适用于复杂驱动壳线，但不适用于实际驱动壳线。
英文摘要：
Building on H. Tran's study of Loewner hulls generated by complex-valued driving functions, which showed the existence of a phase transition, we answer the question of whether the phase transition for complex-driven hulls matches the phase transition for real-driven hulls. This is accomplished through a detailed study of the Loewner hulls generated by driving functions $c\sqrt{1-t}$ and $c\sqrt{τ+ t}$ for $c \in \mathbb{C}$ and $τ\geq 0$. This family also provides examples of new geometric behavior that is possible for complex-driven hulls but prohibited for real-driven hulls.
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