变分卡纳姆-赫尔弗里希流的广义最小化运动

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-12 DOI:10.1515/acv-2022-0056

Katharina Brazda, Martin Kružík, Ulisse Stefanelli

{"title":"变分卡纳姆-赫尔弗里希流的广义最小化运动","authors":"Katharina Brazda, Martin Kružík, Ulisse Stefanelli","doi":"10.1515/acv-2022-0056","DOIUrl":null,"url":null,"abstract":"The gradient flow of the Canham–Helfrich functional is tackled via the generalized minimizing movements approach. We prove the existence of solutions in Wasserstein spaces of varifolds, as well as upper and lower diameter bounds. In the more regular setting of multiply covered <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> {C^{1,1}} surfaces, we provide a Li–Yau-type estimate for the Canham–Helfrich energy and prove the conservation of multiplicity along the evolution.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized minimizing movements for the varifold Canham–Helfrich flow\",\"authors\":\"Katharina Brazda, Martin Kružík, Ulisse Stefanelli\",\"doi\":\"10.1515/acv-2022-0056\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The gradient flow of the Canham–Helfrich functional is tackled via the generalized minimizing movements approach. We prove the existence of solutions in Wasserstein spaces of varifolds, as well as upper and lower diameter bounds. In the more regular setting of multiply covered <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msup> <m:mi>C</m:mi> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> {C^{1,1}} surfaces, we provide a Li–Yau-type estimate for the Canham–Helfrich energy and prove the conservation of multiplicity along the evolution.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/acv-2022-0056\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/acv-2022-0056","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

Canham-Helfrich 函数的梯度流是通过广义最小化运动方法解决的。我们证明了变曲率的瓦瑟斯坦空间中解的存在性，以及直径的上下限。在多面覆盖的 C 1 , 1 {C^{1,1}} 曲面这一更为常规的环境中，我们提供了 Canham-Helfrich 能量的 Li-Yau 型估计，并证明了沿演化过程的多重性守恒。

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

Generalized minimizing movements for the varifold Canham–Helfrich flow

The gradient flow of the Canham–Helfrich functional is tackled via the generalized minimizing movements approach. We prove the existence of solutions in Wasserstein spaces of varifolds, as well as upper and lower diameter bounds. In the more regular setting of multiply covered C 1 , 1

{C^{1,1}}

surfaces, we provide a Li–Yau-type estimate for the Canham–Helfrich energy and prove the conservation of multiplicity along the evolution.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

期刊最新文献

Management of Cholesteatoma: Hearing Rehabilitation. Congenital Cholesteatoma. Evaluation of Cholesteatoma. Management of Cholesteatoma: Extension Beyond Middle Ear/Mastoid. Recidivism and Recurrence.