Plenty of big projections imply big pieces of Lipschitz graphs

• 成果类型: Article
• 署名作者: Orponen, Tuomas
• 署名单位: University of Jyvaskyla
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01055-z
• 发表日期: 2021
• 页码: 653-709
• 关键词: buffons needle; uniform rectifiability; sets

摘要

I prove that closed n-regular sets E subset of R-d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.