关于加权Yamabe流的注释

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-06-02 DOI:10.1134/S1560354723030048

Theodore Yu. Popelensky

{"title":"关于加权Yamabe流的注释","authors":"Theodore Yu. Popelensky","doi":"10.1134/S1560354723030048","DOIUrl":null,"url":null,"abstract":"<div><p>For two dimensional surfaces (smooth) Ricci and Yamabe flows are equivalent.\nIn 2003, Chow and Luo developed the theory of combinatorial Ricci flow for circle packing metrics on closed triangulated surfaces.\nIn 2004, Luo developed a theory of discrete Yamabe flow for closed triangulated surfaces.\nHe investigated the formation of singularities and convergence to a metric of constant curvature.</p><p>In this note we develop the theory of a naïve discrete Ricci flow and its modification — the so-called weighted Ricci flow. We prove that this flow has a rich family of first integrals and is equivalent to a certain modification of Luo’s discrete Yamabe flow.\nWe investigate the types of singularities of solutions for these flows and discuss convergence to a metric of weighted\nconstant curvature.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"28 3","pages":"309 - 320"},"PeriodicalIF":0.8000,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Note on the Weighted Yamabe Flow\",\"authors\":\"Theodore Yu. Popelensky\",\"doi\":\"10.1134/S1560354723030048\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For two dimensional surfaces (smooth) Ricci and Yamabe flows are equivalent.\\nIn 2003, Chow and Luo developed the theory of combinatorial Ricci flow for circle packing metrics on closed triangulated surfaces.\\nIn 2004, Luo developed a theory of discrete Yamabe flow for closed triangulated surfaces.\\nHe investigated the formation of singularities and convergence to a metric of constant curvature.</p><p>In this note we develop the theory of a naïve discrete Ricci flow and its modification — the so-called weighted Ricci flow. We prove that this flow has a rich family of first integrals and is equivalent to a certain modification of Luo’s discrete Yamabe flow.\\nWe investigate the types of singularities of solutions for these flows and discuss convergence to a metric of weighted\\nconstant curvature.</p></div>\",\"PeriodicalId\":752,\"journal\":{\"name\":\"Regular and Chaotic Dynamics\",\"volume\":\"28 3\",\"pages\":\"309 - 320\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-06-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Regular and Chaotic Dynamics\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1560354723030048\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354723030048","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

对于二维表面(光滑)，Ricci流和Yamabe流是等价的。2003年，Chow和Luo发展了封闭三角曲面上圆形堆积度量的组合里奇流理论。2004年，罗提出了一个封闭三角曲面的离散Yamabe流理论。他研究了奇点的形成和收敛到常曲率度规。在本文中，我们发展了naïve离散里奇流理论及其修正-所谓加权里奇流。证明了该流具有丰富的第一积分族，并等价于对Luo离散Yamabe流的某种修正。我们研究了这些流解的奇异性类型，并讨论了收敛到一个加权常曲率度规的问题。

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

A Note on the Weighted Yamabe Flow

For two dimensional surfaces (smooth) Ricci and Yamabe flows are equivalent. In 2003, Chow and Luo developed the theory of combinatorial Ricci flow for circle packing metrics on closed triangulated surfaces. In 2004, Luo developed a theory of discrete Yamabe flow for closed triangulated surfaces. He investigated the formation of singularities and convergence to a metric of constant curvature.

In this note we develop the theory of a naïve discrete Ricci flow and its modification — the so-called weighted Ricci flow. We prove that this flow has a rich family of first integrals and is equivalent to a certain modification of Luo’s discrete Yamabe flow. We investigate the types of singularities of solutions for these flows and discuss convergence to a metric of weighted constant curvature.

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

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.