Non-removability of the Sierpiski gasket
成果类型：
Article
署名作者：
Ntalampekos, Dimitrios
署名单位：
State University of New York (SUNY) System; Stony Brook University
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-00852-3
发表日期：
2019
页码：
519-595
关键词：
摘要：
We prove that the Sierpiski gasket is non-removable for quasiconformal maps, thus answering a question of Bishop (NSF Research Proposal, 2015. http://www.math.stonybrook.edu/similar to bishop/vita/nsf15.pdf). The proof involves a new technique of constructing an exceptional homeomorphism from R-2 into some non-planar surface S, and then embedding this surface quasisymmetrically back into the plane by using the celebrated Bonk-Kleiner Theorem (Bonk and Kleiner in Invent Math 150(1):127-183, 2002). We also prove that all homeomorphic copies of the Sierpiski gasket are non-removable for continuous Sobolev functions of the class W-1,W-p for 1 <= p <= 2, thus complementing and sharpening the results of the author's previous work (Ntalampekos in A removability theorem for Sobolev functions and detour sets. arXiv:1706.07687).
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