On the continuity of SLEκ in κ

• 成果类型: Article
• 署名作者: Viklund, Fredrik Johansson; Rohde, Steffen; Wong, Carto
• 署名单位: Columbia University; University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0506-z
• 发表日期: 2014
• 页码: 413-433
• 关键词: holder regularity; dimension; CURVES

摘要

We prove that for almost every Brownian motion sample, the corresponding SLE curves parameterized by capacity exist and change continuously in the supremum norm when varies in the interval , where . We estimate the -dependent modulus of continuity of the curves and also give an estimate on the modulus of continuity for the supremum norm change with .