Conformal invariants from nodal sets. II: Manifolds with boundary

DOI10.4171/JST/345zbMath1477.58018arXiv1905.06136MaRDI QIDQ2247195

Mikhail Karpukhin, Graham Cox, Yannick Sire, Dmitry Jakobson

Publication date: 17 November 2021

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.06136

zbMATH Keywords

conformal geometryspectral geometrymanifolds with boundarynodal sets

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Differential invariants (local theory), geometric objects (53A55) Other special differential geometries (53A40)

Cites Work

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• Zero and negative eigenvalues of the conformal Laplacian
• Quadratic differentials and conformal invariants
• Fractional Laplacian in conformal geometry
• Invariants of conformal Laplacians
• The classification of simply connected manifolds of positive scalar curvature
• Some inequalities between Dirichlet and Neumann eigenvalues
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• The Yamabe problem on manifolds with boundary
• The space of negative scalar curvature metrics
• Scalar curvature and conformal deformation of Riemannian structure
• Scattering matrix in conformal geometry
• Uniqueness and non-uniqueness of metrics with prescribed scalar and mean curvature on compact manifolds with boundary.
• Critical sets of solutions to elliptic equations.
• Barycenter technique and the Riemann mapping problem of Cherrier-Escobar
• Conformal metrics with prescribed mean curvature on the boundary
• Nullspaces of conformally invariant operators. Applications to \(Q_k\)-curvature
• On the topology of moduli space of negative constant scalar curvature metrics on a Haken manifold
• Curvature functions for compact 2-manifolds
• Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary
• Second eigenvalue of the Yamabe operator and applications
• On Fractional GJMS Operators
• Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription
• Conformally Invariant Powers of the Laplacian, I: Existence
• Geometric measure of singular sets of elliptic equations
• Boundary operators associated with the Paneitz operator