Regularity of the SLE(4) uniformizing map and the SLE(8) trace

With Konstantinos Kavvadias (Cambridge)

Regularity of the SLE(4) uniformizing map and the SLE(8) trace

We give the modulus of continuity of the SLE (4) uniformizing map. As a consequence of our analysis, we show that the Jones-Smirnov condition for conformal removability does not hold for SLE (4). We also give the modulus of continuity for SLE (8) with the capacity parameterization, proving a conjecture of Alvisio and Lawler.

Based on joint work with Jason Miller and Lukas Schoug.

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