`a`
Electronic Research Announcements in Mathematical Sciences (ERA-MS)
 

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

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

 
       Abstract        References        Full Text (354.7K)              Related Articles       

Yaiza Canzani - Department of Mathematics and Statistics, McGill University, Montréal, Canada (email)
A. Rod Gover - Department of Mathematics, University of Auckland, New Zealand &, Mathematical Sciences Institute, Australian National University, Canberra, Australia (email)
Dmitry Jakobson - Department of Mathematics and Statistics, McGill University, Montréal, Canada (email)
Raphaël Ponge - Department of Mathematical Sciences, Seoul National University, Seoul, South Korea (email)

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.

Keywords:  Spectral geometry, conformal geometry, nodal sets, Qk-curvature.
Mathematics Subject Classification:  58J50, 53A30, 53A55, 53C21.

Received: June 2012;      Revised: March 2013;      Available Online: March 2013.

 References