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

Remarks on Loewner Chains Driven by Finite Variation Functions