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Density problems on vector bundles and manifolds


Author: Lashi Bandara
Journal: Proc. Amer. Math. Soc. 142 (2014), 2683-2695
MSC (2010): Primary 46E35, 53C21, 58J60
DOI: https://doi.org/10.1090/S0002-9939-2014-12284-2
Published electronically: April 22, 2014
MathSciNet review: 3209324
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Abstract: We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators. Furthermore, we show that smooth, compactly supported functions are dense in second order Sobolev spaces on such manifolds under the sole additional assumption that the Ricci curvature is uniformly bounded from below.


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Additional Information

Lashi Bandara
Affiliation: Centre for Mathematics and its Applications, Australian National University, Canberra, ACT, 0200, Australia
Email: lashi.bandara@anu.edu.au

DOI: https://doi.org/10.1090/S0002-9939-2014-12284-2
Keywords: Density problems, first order operators on vector bundles, Laplacian on vector bundles, second order Sobolev spaces on manifolds
Received by editor(s): August 20, 2012
Published electronically: April 22, 2014
Communicated by: James E. Colliander
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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