Almost monotonicity formula for H-minimal Legendrian surfaces in the Heisenberg group

IF 3.1 1区 数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2023-10-03 DOI:10.1002/cpa.22179
Tristan Rivière
{"title":"Almost monotonicity formula for H-minimal Legendrian surfaces in the Heisenberg group","authors":"Tristan Rivière","doi":"10.1002/cpa.22179","DOIUrl":null,"url":null,"abstract":"<p>We prove an almost monotonicity formula for H-minimal Legendrian Surfaces (also called <i>contact stationary Legendrian immersions</i> or <i>Hamiltonian stationary immersions</i>) in the Heisenberg Group <math>\n <semantics>\n <msup>\n <mi>H</mi>\n <mn>2</mn>\n </msup>\n <annotation>${\\mathbb {H}}^2$</annotation>\n </semantics></math>. From this formula we deduce a Bernstein-Liouville type theorem for H-minimal Legendrian Surfaces. We also present some possible range of applications of this formula.</p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"77 3","pages":"1940-1957"},"PeriodicalIF":3.1000,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22179","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22179","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: 0

Abstract

We prove an almost monotonicity formula for H-minimal Legendrian Surfaces (also called contact stationary Legendrian immersions or Hamiltonian stationary immersions) in the Heisenberg Group H 2 ${\mathbb {H}}^2$ . From this formula we deduce a Bernstein-Liouville type theorem for H-minimal Legendrian Surfaces. We also present some possible range of applications of this formula.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
海森堡群中H-极小勒让德曲面的几乎单调性公式
我们证明了海森堡群H2${\mathbb{H}}^2$中H-极小勒让德曲面(也称为接触平稳勒让德浸入或哈密顿平稳浸入)的几乎单调性公式。从这个公式我们推导出H-极小Legendarian曲面的Bernstein—Liouville型定理。我们还介绍了这个公式的一些可能的应用范围。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
6.70
自引率
3.30%
发文量
59
审稿时长
>12 weeks
期刊介绍: Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.
期刊最新文献
On the Read‐Shockley energy for grain boundaries in 2D polycrystals Issue Information - TOC Analysis of density matrix embedding theory around the non‐interacting limit Special Lagrangian pair of pants Localized and degenerate controls for the incompressible Navier–Stokes system
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1