Nullspaces of conformally invariant operators. Applications to $\boldsymbol{Q_k}$-curvature

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2013-03-01 DOI:10.3934/ERA.2013.20.43

Y. Canzani, A. Gover, D. Jakobson, Raphael Ponge

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.

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共形不变算子的零空间。$\boldsymbol{Q_k}$-曲率的应用

研究了保形协变微分算子零空间中函数的保形不变量。不变量包括GJMS算子核中特征函数的节点集和节点域拓扑。我们建立了在任意维度$n\geq 3$的流形上，存在许多度量的不变量是非平凡的。讨论了曲率处方问题的新应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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