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Conformal invariants from nodal sets. II. Manifolds with boundary

Cox, Graham and Jakobson, Dmitry and Karpukhin, Mikhail and Sire, Yannick (2021) Conformal invariants from nodal sets. II. Manifolds with boundary. Journal of Spectral Theory, 11 (2). pp. 387-409. ISSN 1664-039X. doi:10.4171/jst/345.

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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.

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Additional Information:© 2021 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license. Received May 13, 2019. Published online: 2021-03-12. Graham Cox acknowledges the support of NSERC grant RGPIN-2017-04259. Dmitry Jakobson was supported by NSERC and FQRNT grants and Peter Redpath Fellowship of McGill University (Canada). Mikhail Karpukhin was supported by Schulich Fellowship of McGill University (Canada) at initial stages of this project. The authors would like to thank Asma Hassannezhad and A. Rod Gover for stimulating discussions and very interesting remarks about preliminary versions of this paper. In addition, the authors would like to thank Ailana Fraser, Pengfei Guan and Richard Schoen for useful discussions. The authors would like to thank BIRS, CRM, Oberwolfach, McGill and Johns Hopkins University for their hospitality.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2017-04259
Fonds de recherche du Québec - Nature et technologies (FRQNT)UNSPECIFIED
McGill UniversityUNSPECIFIED
Subject Keywords:Spectral geometry, conformal geometry, nodal sets, manifolds with boundary
Issue or Number:2
Classification Code:Mathematics Subject Classification (2010): 58J50, 53A30, 53A55, 53C21
Record Number:CaltechAUTHORS:20210821-171517071
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Official Citation:Cox Graham, Jakobson Dmitry, Karpukhin Mikhail, Sire Yannick: Conformal invariants from nodal sets. II. Manifolds with boundary. J. Spectr. Theory 11 (2021), 387-409. doi: 10.4171/JST/345
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110373
Deposited By: Tony Diaz
Deposited On:21 Aug 2021 17:25
Last Modified:21 Aug 2021 17:25

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