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{"title":"在ℍ2 × ℝ空间的最小曲面上","authors":"Bendehiba Senoussi","doi":"10.1515/gmj-2024-2038","DOIUrl":null,"url":null,"abstract":"A surface is minimal if the mean curvature <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">ℋ</m:mi> <m:mi>mean</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2038_eq_0115.png\"/> <jats:tex-math>{\\mathcal{H}_{\\rm mean}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> vanishes everywhere. In this paper, we study some surfaces in the product space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>ℍ</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo>×</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2038_eq_0102.png\"/> <jats:tex-math>{\\mathbb{H}^{2}\\times\\mathbb{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In particular, we completely classify minimal surfaces.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On minimal surfaces in ℍ2 × ℝ space\",\"authors\":\"Bendehiba Senoussi\",\"doi\":\"10.1515/gmj-2024-2038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A surface is minimal if the mean curvature <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:msub> <m:mi mathvariant=\\\"script\\\">ℋ</m:mi> <m:mi>mean</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2038_eq_0115.png\\\"/> <jats:tex-math>{\\\\mathcal{H}_{\\\\rm mean}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> vanishes everywhere. In this paper, we study some surfaces in the product space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mrow> <m:msup> <m:mi>ℍ</m:mi> <m:mn>2</m:mn> </m:msup> <m:mo>×</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_gmj-2024-2038_eq_0102.png\\\"/> <jats:tex-math>{\\\\mathbb{H}^{2}\\\\times\\\\mathbb{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In particular, we completely classify minimal surfaces.\",\"PeriodicalId\":55101,\"journal\":{\"name\":\"Georgian Mathematical Journal\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Georgian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/gmj-2024-2038\",\"RegionNum\":4,\"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":"Georgian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/gmj-2024-2038","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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