{"paper":{"title":"Optimal H\\\"older Continuity and Dimension Properties for SLE with Minkowski Content Parametrization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dapeng Zhan","submitted_at":"2017-06-18T03:04:32Z","abstract_excerpt":"We make use of the fact that a two-sided whole-plane Schramm-Loewner evolution (SLE$_\\kappa$) curve $\\gamma$ for $\\kappa\\in(0,8)$ from $\\infty$ to $\\infty$ through $0$ may be parametrized by its $d$-dimensional Minkowski content, where $d=1+\\frac\\kappa 8$, and become a self-similar process of index $\\frac 1d$ with stationary increments. We prove that such $\\gamma$ is locally $\\alpha$-H\\\"older continuous for any $\\alpha<\\frac 1d$. In the case $\\kappa\\in(0,4]$, we show that $\\gamma$ is not locally $\\frac 1d$-H\\\"older continuous. We also prove that, for any deterministic closed set $A\\subset \\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05603","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}