Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, Seunghyeok | - |
dc.contributor.author | Musso, Monica | - |
dc.contributor.author | Wei, Juncheng | - |
dc.date.accessioned | 2022-07-06T11:46:28Z | - |
dc.date.available | 2022-07-06T11:46:28Z | - |
dc.date.created | 2021-05-11 | - |
dc.date.issued | 2021-11 | - |
dc.identifier.issn | 0294-1449 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/140602 | - |
dc.description.abstract | We concern C2-compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are 4, 5 or 6. By conducting a quantitative analysis of a linear equation associated with the problem, we prove that the trace-free second fundamental form must vanish at possible blow-up points of a sequence of blowing-up solutions. Applying this result and the positive mass theorem, we deduce the C2-compactness for all 4-manifolds (which may be non-umbilic). For the 5-dimensional case, we also establish that a sum of the second-order derivatives of the trace-free second fundamental form is non-negative at possible blow-up points. We essentially use this fact to obtain the C2-compactness for all 5-manifolds. Finally, we show that the C2-compactness on 6-manifolds is true if the trace-free second fundamental form on the boundary never vanishes. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | ELSEVIER | - |
dc.title | Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Seunghyeok | - |
dc.identifier.doi | 10.1016/j.anihpc.2021.01.005 | - |
dc.identifier.scopusid | 2-s2.0-85101686545 | - |
dc.identifier.wosid | 000709109300005 | - |
dc.identifier.bibliographicCitation | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, v.38, no.6, pp.1763 - 1793 | - |
dc.relation.isPartOf | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | - |
dc.citation.title | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | - |
dc.citation.volume | 38 | - |
dc.citation.number | 6 | - |
dc.citation.startPage | 1763 | - |
dc.citation.endPage | 1793 | - |
dc.type.rims | ART | - |
dc.type.docType | Article in Press | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | Y | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.subject.keywordPlus | BLOW-UP PHENOMENA | - |
dc.subject.keywordPlus | YAMABE PROBLEM | - |
dc.subject.keywordPlus | UNIQUENESS THEOREMS | - |
dc.subject.keywordPlus | EXISTENCE THEOREM | - |
dc.subject.keywordPlus | DEFORMATIONS | - |
dc.subject.keywordPlus | EQUATIONS | - |
dc.subject.keywordAuthor | Boundary Yamabe problem | - |
dc.subject.keywordAuthor | Compactness | - |
dc.subject.keywordAuthor | Blow-up analysis | - |
dc.subject.keywordAuthor | Positive mass theorem | - |
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