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arXiv · 1710.07302

Remarks on Loewner Chains Driven by Finite Variation Functions

Atul Shekhar·Huy Tran·Yilin Wang
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Abstract

To explore the relation between properties of Loewner chains and properties of their driving functions, we study Loewner chains driven by functions $U$ of finite total variation. Under some appropriate conditions, we show existence of the simple trace $\gamma$ and establish continuity of the map $U$ to $\gamma$ with respect to uniform topology on $\gamma$ and the total variation topology on $U$. In the spirit of work of Wong and Tran-Lind, we also obtain conditions on the driving function that ensures the trace to be continuously differentiable.

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Atul Shekhar, Huy Tran, Yilin Wang. 2017-10-19. Remarks on Loewner Chains Driven by Finite Variation Functions. https://doi.org/10.5186/aasfm.2019.4421

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