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arXiv · 1409.5212

Self-adjointness of the Gaffney Laplacian on vector bundles

Lashi Bandara·Ognjen Milatovic
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Abstract

We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.

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Lashi Bandara, Ognjen Milatovic. 2015-05-25. Self-adjointness of the Gaffney Laplacian on vector bundles. https://doi.org/10.1007/s11040-015-9188-3

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