DC Field | Value | Language |
---|---|---|
dc.contributor.author | Oh, Yong-Geun | - |
dc.date.accessioned | 2023-07-11T01:45:23Z | - |
dc.date.available | 2023-07-11T01:45:23Z | - |
dc.date.created | 2023-02-02 | - |
dc.date.issued | 2022-01 | - |
dc.identifier.issn | 1664-3607 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/117919 | - |
dc.description.abstract | © 2022 The Author(s).In [Y.-G. Oh and R. Wang, Analysis of contact Cauchy-Riemann maps I: A priori Ck estimates and asymptotic convergence, Osaka J. Math. 55(4) (2018) 647-679; Y.-G. Oh and R. Wang, Analysis of contact Cauchy-Riemann maps II: Canonical neighborhoods and exponential convergence for the Morse-Bott case, Nagoya Math. J. 231 (2018) 128-223], the authors studied the nonlinear elliptic system w = 0,d(w λ j) = 0 without involving symplectization for each given contact triad (Q,λ,J), and established the a priori Wk,2 elliptic estimates and proved the asymptotic (subsequence) convergence of the map w: ς˙ → Q for any solution, called a contact instanton, on ς˙ under the hypothesis w λ C0 < ∞ and d w L2 L4. The asymptotic limit of a contact instanton is a 'spiraling' instanton along a 'rotating' Reeb orbit near each puncture on a punctured Riemann surface ς˙. Each limiting Reeb orbit carries a 'charge' arising from the integral of w λ j. In this paper, we further develop analysis of contact instantons, especially the W1,p estimate for p > 2 (or the C1-estimate), which is essential for the study of compactification of the moduli space and the relevant Fredholm theory for contact instantons. In particular, we define a Hofer-type off-shell energy Eλ(j,w) for any pair (j,w) with a smooth map w satisfying d(w λ j) = 0, and develop the bubbling-off analysis and prove an -regularity result. We also develop the relevant Fredholm theory and carry out index calculations (for the case of vanishing charge). | - |
dc.language | English | - |
dc.publisher | World Scientific | - |
dc.relation.isPartOf | Bulletin of Mathematical Sciences | - |
dc.title | Analysis of contact Cauchy-Riemann maps III: Energy, bubbling and Fredholm theory | - |
dc.type | Article | - |
dc.identifier.doi | 10.1142/S1664360722500114 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | Bulletin of Mathematical Sciences | - |
dc.identifier.wosid | 000895399200001 | - |
dc.citation.title | Bulletin of Mathematical Sciences | - |
dc.contributor.affiliatedAuthor | Oh, Yong-Geun | - |
dc.identifier.scopusid | 2-s2.0-85144316310 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article; Early Access | - |
dc.subject.keywordPlus | PSEUDO-HOLOMORPHIC-CURVES | - |
dc.subject.keywordPlus | WEINSTEIN CONJECTURE | - |
dc.subject.keywordPlus | INDEX | - |
dc.subject.keywordPlus | EXISTENCE | - |
dc.subject.keywordAuthor | -regularity theorem | - |
dc.subject.keywordAuthor | asymptotic Hick&apos | - |
dc.subject.keywordAuthor | s field | - |
dc.subject.keywordAuthor | bubbling-off analysis | - |
dc.subject.keywordAuthor | contact instanton (action, charge and potential) | - |
dc.subject.keywordAuthor | Contact manifolds | - |
dc.subject.keywordAuthor | Fredholm theory | - |
dc.subject.keywordAuthor | Hofer-type energy | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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