{"title":"沉入稳定超曲面的正切圆锥的唯一性","authors":"Nick Edelen, Paul Minter","doi":"10.1007/s00205-024-02071-y","DOIUrl":null,"url":null,"abstract":"<div><p>We establish uniqueness and regularity results for tangent cones (at a point or at infinity), with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In particular, our results allow the tangent cone to occur with any integer multiplicity.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"248 6","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-02071-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Uniqueness of Regular Tangent Cones for Immersed Stable Hypersurfaces\",\"authors\":\"Nick Edelen, Paul Minter\",\"doi\":\"10.1007/s00205-024-02071-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We establish uniqueness and regularity results for tangent cones (at a point or at infinity), with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In particular, our results allow the tangent cone to occur with any integer multiplicity.</p></div>\",\"PeriodicalId\":55484,\"journal\":{\"name\":\"Archive for Rational Mechanics and Analysis\",\"volume\":\"248 6\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00205-024-02071-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Rational Mechanics and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00205-024-02071-y\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-024-02071-y","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Uniqueness of Regular Tangent Cones for Immersed Stable Hypersurfaces
We establish uniqueness and regularity results for tangent cones (at a point or at infinity), with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In particular, our results allow the tangent cone to occur with any integer multiplicity.
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The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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