WDC集并集的曲率

IF 0.8 3区数学 Q2 MATHEMATICS Mathematika Pub Date : 2023-05-04 DOI:10.1112/mtk.12195

Dušan Pokorný

{"title":"WDC集并集的曲率","authors":"Dušan Pokorný","doi":"10.1112/mtk.12195","DOIUrl":null,"url":null,"abstract":"<p>We prove the existence of the curvature measures for a class of <math>\n <semantics>\n <msub>\n <mi>U</mi>\n <mi>WDC</mi>\n </msub>\n <annotation>${\\mathcal {U}}_{{\\rm WDC}}$</annotation>\n </semantics></math> sets, which is a direct generalisation of <math>\n <semantics>\n <msub>\n <mi>U</mi>\n <mrow>\n <mi>P</mi>\n <mspace></mspace>\n <mi>R</mi>\n </mrow>\n </msub>\n <annotation>${\\mathcal {U}}_{\\rm {P\\! R}}$</annotation>\n </semantics></math> sets studied by Rataj and Zähle. Moreover, we provide a simple characterisation of <math>\n <semantics>\n <msub>\n <mi>U</mi>\n <mi>WDC</mi>\n </msub>\n <annotation>${\\mathcal {U}}_{{\\rm WDC}}$</annotation>\n </semantics></math> sets in <math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mn>2</mn>\n </msup>\n <annotation>$\\mathbb {R}^2$</annotation>\n </semantics></math> and prove that in <math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mn>2</mn>\n </msup>\n <annotation>$\\mathbb {R}^2$</annotation>\n </semantics></math>, the class of <math>\n <semantics>\n <msub>\n <mi>U</mi>\n <mi>WDC</mi>\n </msub>\n <annotation>${\\mathcal {U}}_{{\\rm WDC}}$</annotation>\n </semantics></math> sets contains essentially all classes of sets known to admit curvature measures.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Curvatures for unions of WDC sets\",\"authors\":\"Dušan Pokorný\",\"doi\":\"10.1112/mtk.12195\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove the existence of the curvature measures for a class of <math>\\n <semantics>\\n <msub>\\n <mi>U</mi>\\n <mi>WDC</mi>\\n </msub>\\n <annotation>${\\\\mathcal {U}}_{{\\\\rm WDC}}$</annotation>\\n </semantics></math> sets, which is a direct generalisation of <math>\\n <semantics>\\n <msub>\\n <mi>U</mi>\\n <mrow>\\n <mi>P</mi>\\n <mspace></mspace>\\n <mi>R</mi>\\n </mrow>\\n </msub>\\n <annotation>${\\\\mathcal {U}}_{\\\\rm {P\\\\! R}}$</annotation>\\n </semantics></math> sets studied by Rataj and Zähle. Moreover, we provide a simple characterisation of <math>\\n <semantics>\\n <msub>\\n <mi>U</mi>\\n <mi>WDC</mi>\\n </msub>\\n <annotation>${\\\\mathcal {U}}_{{\\\\rm WDC}}$</annotation>\\n </semantics></math> sets in <math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mn>2</mn>\\n </msup>\\n <annotation>$\\\\mathbb {R}^2$</annotation>\\n </semantics></math> and prove that in <math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mn>2</mn>\\n </msup>\\n <annotation>$\\\\mathbb {R}^2$</annotation>\\n </semantics></math>, the class of <math>\\n <semantics>\\n <msub>\\n <mi>U</mi>\\n <mi>WDC</mi>\\n </msub>\\n <annotation>${\\\\mathcal {U}}_{{\\\\rm WDC}}$</annotation>\\n </semantics></math> sets contains essentially all classes of sets known to admit curvature measures.</p>\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12195\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12195","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了一类UWDC${\mathcal {U}}_{\rm WDC}}$集合的曲率测度的存在性，它是UPR${\mathcal {U}}_{\rm {P\!R}}$集合由Rataj和Zähle研究。此外，我们给出了R2$\mathbb {R}^2$中的UWDC${\mathcal {U}}_{\rm WDC}}$集合的一个简单刻画，并证明了在R2$\mathbb {R}^2$中，UWDC${\mathcal {U}}_{\rm WDC}}$集合本质上包含了所有已知允许曲率测度的集合类。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Curvatures for unions of WDC sets

We prove the existence of the curvature measures for a class of $U_{WDC}$ sets, which is a direct generalisation of $U_{P R}$ sets studied by Rataj and Zähle. Moreover, we provide a simple characterisation of $U_{WDC}$ sets in $R^{2}$ and prove that in $R^{2}$ , the class of $U_{WDC}$ sets contains essentially all classes of sets known to admit curvature measures.

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

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.

期刊最新文献

Twisted mixed moments of the Riemann zeta function Diophantine approximation by rational numbers of certain parity types Issue Information The local solubility for homogeneous polynomials with random coefficients over thin sets A discrete mean value of the Riemann zeta function