RCD空间上调和函数的强唯一延拓失效

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2022-04-29 DOI:10.1515/crelle-2022-0090

Qintao Deng, Xinrui Zhao

{"title":"RCD空间上调和函数的强唯一延拓失效","authors":"Qintao Deng, Xinrui Zhao","doi":"10.1515/crelle-2022-0090","DOIUrl":null,"url":null,"abstract":"Abstract Unique continuation of harmonic functions on RCD {\\operatorname{RCD}} space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on RCD ⁡ ( K , 2 ) {\\operatorname{RCD}(K,2)} spaces and give a counterexample for strong unique continuation in the setting of RCD ⁡ ( K , N ) {\\operatorname{RCD}(K,N)} space for any N ≥ 4 {N\\geq 4} and any K ∈ ℝ {K\\in\\mathbb{R}} .","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Failure of strong unique continuation for harmonic functions on RCD spaces\",\"authors\":\"Qintao Deng, Xinrui Zhao\",\"doi\":\"10.1515/crelle-2022-0090\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Unique continuation of harmonic functions on RCD {\\\\operatorname{RCD}} space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on RCD ⁡ ( K , 2 ) {\\\\operatorname{RCD}(K,2)} spaces and give a counterexample for strong unique continuation in the setting of RCD ⁡ ( K , N ) {\\\\operatorname{RCD}(K,N)} space for any N ≥ 4 {N\\\\geq 4} and any K ∈ ℝ {K\\\\in\\\\mathbb{R}} .\",\"PeriodicalId\":54896,\"journal\":{\"name\":\"Journal fur die Reine und Angewandte Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal fur die Reine und Angewandte Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2022-0090\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal fur die Reine und Angewandte Mathematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/crelle-2022-0090","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

RCD {\operatorname{RCD}}空间上调和函数的唯一延拓是一个长期存在的开放问题，即使在Alexandrov空间中也鲜为人知。本文建立了RCD (K,2) {\operatorname{RCD} (K,2)}空间上调和函数的弱唯一延拓定理，并给出了RCD (K,N) {\operatorname{RCD} (K,N)}空间对任意N≥4n {\geq 4}和任意K∈∈K{\in\mathbb{R}}的强唯一延拓的一个反例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Failure of strong unique continuation for harmonic functions on RCD spaces

Abstract Unique continuation of harmonic functions on RCD {\operatorname{RCD}} space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on RCD ⁡ ( K , 2 ) {\operatorname{RCD}(K,2)} spaces and give a counterexample for strong unique continuation in the setting of RCD ⁡ ( K , N ) {\operatorname{RCD}(K,N)} space for any N ≥ 4 {N\geq 4} and any K ∈ ℝ {K\in\mathbb{R}} .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.