{"title":"将多谐超曲面转化为复杂空间形式","authors":"José Miguel Balado-Alves","doi":"10.1007/s10231-024-01452-0","DOIUrl":null,"url":null,"abstract":"<div><p>We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for <span>\\(\\mathbb{C}\\mathbb{P}^n\\)</span> and <span>\\(\\mathbb{C}\\mathbb{H}^n\\)</span>, respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 6","pages":"2463 - 2480"},"PeriodicalIF":1.0000,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01452-0.pdf","citationCount":"0","resultStr":"{\"title\":\"Polyharmonic hypersurfaces into complex space forms\",\"authors\":\"José Miguel Balado-Alves\",\"doi\":\"10.1007/s10231-024-01452-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for <span>\\\\(\\\\mathbb{C}\\\\mathbb{P}^n\\\\)</span> and <span>\\\\(\\\\mathbb{C}\\\\mathbb{H}^n\\\\)</span>, respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":\"203 6\",\"pages\":\"2463 - 2480\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10231-024-01452-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-024-01452-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01452-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Polyharmonic hypersurfaces into complex space forms
We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for \(\mathbb{C}\mathbb{P}^n\) and \(\mathbb{C}\mathbb{H}^n\), respectively. Moreover, we study the stability of biharmonic hypersurfaces and compute the normal index for a large family of solutions.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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