SLE_4统一化映射的正则性及SLE_8轨迹
Regularity of the SLE$_4$ uniformizing map and the SLE$_8$ trace
AI总结：
研究SLE_4统一化映射的连续模，证明其为( log δ^{-1} )^{-1/3 + o(1)}，并展示SLE_4不满足Jones-Smirnov条件。同时证明SLE_8的连续模为( log δ^{-1} )^{-1/4 + o(1)}，验证Alvisio和Lawler的猜想。
摘要：
我们证明SLE_4统一化映射的连续模在δ→0时为(log δ^{-1})^{-1/3+o(1)}。作为分析结果，我们展示Jones-Smirnov条件（带有准超几何测地线）对于SLE_4不成立。我们还证明SLE_8在容量时间参数化下的连续模为(log δ^{-1})^{-1/4+o(1)}，证明了Alvisio和Lawler的猜想。
英文摘要：
We show that the modulus of continuity of the SLE$_4$ uniformizing map is given by $(\log δ^{-1})^{-1/3+o(1)}$ as $δ\to 0$. As a consequence of our analysis, we show that the Jones-Smirnov condition for conformal removability (with quasihyperbolic geodesics) does not hold for SLE$_4$. We also show that the modulus of continuity for SLE$_8$ with the capacity time parameterization is given by $(\log δ^{-1})^{-1/4+o(1)}$ as $δ\to 0$, proving a conjecture of Alvisio and Lawler.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
