{"title":"Nullspaces of conformally invariant operators. Applications to $\\boldsymbol{Q_k}$-curvature","authors":"Y. Canzani, A. Gover, D. Jakobson, Raphael Ponge","doi":"10.3934/ERA.2013.20.43","DOIUrl":null,"url":null,"abstract":"We study conformal invariants that arise from functions in the \nnullspace of conformally covariant differential operators. \nThe invariants include nodal sets and the topology of nodal domains \nof eigenfunctions in the kernel of GJMS operators. We establish \nthat on any manifold of dimension $n\\geq 3$, there exist many metrics \nfor which our invariants are nontrivial. We discuss new applications \nto curvature prescription problems.","PeriodicalId":53151,"journal":{"name":"Electronic Research Announcements in Mathematical Sciences","volume":"20 1","pages":"43-50"},"PeriodicalIF":0.0000,"publicationDate":"2013-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Research Announcements in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/ERA.2013.20.43","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
We study conformal invariants that arise from functions in the
nullspace of conformally covariant differential operators.
The invariants include nodal sets and the topology of nodal domains
of eigenfunctions in the kernel of GJMS operators. We establish
that on any manifold of dimension $n\geq 3$, there exist many metrics
for which our invariants are nontrivial. We discuss new applications
to curvature prescription problems.
期刊介绍：
Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication.
ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007
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