Conformal invariants from nodal sets. II. Manifolds with boundary

Creators: Cox, Graham; Jakobson, Dmitry; Karpukhin, Mikhail; Sire, Yannick

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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.

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.

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