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Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription

Canzani, Yaiza; Gover, Rod; Jakobson, Dmitry; Ponge, Raphael


In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our...[Show more]

CollectionsANU Research Publications
Date published: 2013
Type: Journal article
Source: International Mathematics Research Notices
DOI: 10.1093/imrn/rns295


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