Conformal invariants from nodal sets. II. Manifolds with boundary

Graham Cox, Dmitry Jakobson, Mikhail Karpukhin, Yannick Sire

Type: Article

Publication Date: 2021-03-12

Citations: 0

DOI: https://doi.org/10.4171/jst/345

Abstract

In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators on manifolds with boundary. We also consider applications to curvature prescription problems on manifolds with boundary. We relate Dirichlet and Neumann eigenvalues and put the results developed here for the Escobar problem into the more general framework of boundary operators of arbitrary order.

Locations

Journal of Spectral Theory - View - PDF
arXiv (Cornell University) - View - PDF
CaltechAUTHORS (California Institute of Technology) - View - PDF

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Works Cited by This (28)

Action	Title	Year	Authors
+ PDF Chat	Invariants of conformal Laplacians	1987	Thomas H. Parker Steven Rosenberg
+ PDF Chat	The Yamabe problem on manifolds with boundary	1992	José F. Escobar
+ PDF Chat	Scalar curvature and conformal deformation of Riemannian structure	1975	Jerry L. Kazdan F. W. Warner
+	Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions	2009	Szu-yu Sophie Chen
+ PDF Chat	Critical sets of solutions to elliptic equations	1999	Robert Hardt M. Hoffmann-Ostenhof Thomas Hoffmann-Ostenhof Nikolaï Nadirashvili
+ PDF Chat	On the topology of the moduli space of negative constant scalar curvature metrics on a Haken manifold	1999	Minyo Katagiri
+	Some Nonlinear Problems in Riemannian Geometry	1998	Thierry Aubin
+ PDF Chat	Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary	2007	Fernando C. Marques
+ PDF Chat	Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription	2013	Yaiza Canzani R. Gover Dmitry Jakobson Raphaël Ponge
+	Curvature Functions for Compact 2-Manifolds	1974	Jerry L. Kazdan F. W. Warner