{"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":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"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":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22179","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","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 . 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.
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