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arXiv · 1509.08342

Boundary operators associated to the Paneitz operator

Jeffrey S. Case
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Abstract

We describe a set of conformally covariant boundary operators associated to the Paneitz operator, in the sense that they give rise to a conformally covariant energy functional for the Paneitz operator on a compact Riemannian manifold with boundary. These operators naturally give rise to a first- and third-order conformally covariant pseudodifferential operator. In the setting of Poincar\'e--Einstein manifolds, we show that these operators agree with the fractional GJMS operators of Graham and Zworski. We also use our operators to establish some new sharp Sobolev trace inequalities.

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Jeffrey S. Case. 2015-09-28. Boundary operators associated to the Paneitz operator. https://arxiv.org/abs/1509.08342

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