Nullspaces of Conformally Invariant Operators. Applications to\n Q_k-curvature

2012/06/04 by Yaiza Canzani, A. Rod Gover, Canzani, Yaiza +5 · 1 citation
Mathematics · Medicine · #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.1206.0517

Abstract

We study conformal invariants that arise from functions in the nullspace of\nconformally covariant differential operators. The invariants include nodal sets\nand the topology of nodal domains of eigenfunctions in the kernel of GJMS\noperators. We establish that on any manifold of dimension n\≥ 3, there\nexist many metrics for which our invariants are nontrivial. We discuss new\napplications to curvature prescription problems.\n

Cited by

• Calculus and invariants on almost complex manifolds, including projective and conformal geometry

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• Admissible Q-curvatures under isometries for the conformal GJMS operators