Conformal removability of non-simple Schramm-Loewner evolutions
| Autor: | Kavvadias, Konstantinos, Miller, Jason, Schoug, Lukas |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider the Schramm-Loewner evolution (SLE$_\kappa$) for $\kappa \in (4,8)$, which is the regime that the curve is self-intersecting but not space-filling. We let ${\mathcal K}$ be the set of $\kappa \in (4,8)$ for which the adjacency graph of connected components of the complement of an SLE$_\kappa$ is a.s. connected, meaning that for every pair of complementary components $U, V$ there exist complementary components $U_1,\ldots,U_n$ with $U_1 = U$, $U_n = V$, and $\partial U_i \cap \partial U_{i+1} \neq \emptyset$ for each $1 \leq i \leq n-1$. We show that the range of an SLE$_\kappa$ for $\kappa \in {\mathcal K}$ is a.s. conformally removable, which answers a question of Sheffield. As a step in the proof, we construct the canonical conformally covariant volume measure on the cut points of an SLE$_\kappa$ for $\kappa \in (4,8)$ and establish a precise upper bound on the measure that it assigns to any Borel set in terms of its diameter. Comment: 71 pages, 6 figures |
| Databáze: | arXiv |
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