Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription
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Canzani, Yaiza; Gover, Rod; Jakobson, Dmitry; Ponge, Raphael
Description
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]
Collections | ANU Research Publications |
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Date published: | 2013 |
Type: | Journal article |
URI: | http://hdl.handle.net/1885/25617 |
Source: | International Mathematics Research Notices |
DOI: | 10.1093/imrn/rns295 |
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