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

Yaiza Canzani; A. Rod Gover; Dmitry Jakobson; Raphaël Ponge

doi:10.3934/era.2013.20.43

Article Contents

2013, Volume 20: 43-50. Doi: 10.3934/era.2013.20.43

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

1.
Department of Mathematics and Statistics, McGill University, Montréal
2.
Department of Mathematics, University of Auckland, New Zealand &, Mathematical Sciences Institute, Australian National University, Canberra
3.
Department of Mathematical Sciences, Seoul National University, Seoul

Received: June 2012

Revised: March 2013

Published: January 2013

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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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Mathematics Subject Classification: 58J50, 53A30, 53A55, 53C21.

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