For κ in K (where the adjacency graph of SLE_κ complementary components is a.s. connected), the range of SLE_κ is a.s. conformally removable; a conformally covariant measure on cut points is constructed as an intermediate step.
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Modulus of continuity for SLE4 uniformizing map is (log δ^{-1})^{-1/3+o(1)}; for SLE8 trace it is (log δ^{-1})^{-1/4+o(1)} as δ→0.
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Conformal removability of non-simple Schramm-Loewner evolutions
For κ in K (where the adjacency graph of SLE_κ complementary components is a.s. connected), the range of SLE_κ is a.s. conformally removable; a conformally covariant measure on cut points is constructed as an intermediate step.
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Regularity of the SLE$_4$ uniformizing map and the SLE$_8$ trace
Modulus of continuity for SLE4 uniformizing map is (log δ^{-1})^{-1/3+o(1)}; for SLE8 trace it is (log δ^{-1})^{-1/4+o(1)} as δ→0.