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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

A model form for exact $b$-metrics


Author: M. S. Joshi
Journal: Proc. Amer. Math. Soc. 129 (2001), 581-584
MSC (2000): Primary 58J50
Published electronically: August 28, 2000
MathSciNet review: 1707151
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Abstract | References | Similar Articles | Additional Information

Abstract:

Any manifold with boundary can be equipped with a $b$-metric which takes the form $\frac{dx^2}{x^2} + h(x,y,dx,dy)$ with respect to some product decomposition near the boundary, and $h$ positive definite on restriction to the tangent space of the boundary. Here we show the existence of a product decomposition such that $h$ is independent of $dx$ modulo terms vanishing to infinite order at the boundary. The uniqueness of this decomposition is also examined.


References [Enhancements On Off] (What's this?)

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Additional Information

M. S. Joshi
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England, United Kingdom
Address at time of publication: NatWest Group Risk, 135 Bishopsgate, London EC2M 3UR, England, United Kingdom
Email: joshi@dpmms.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05599-4
PII: S 0002-9939(00)05599-4
Keywords: Scattering theory, model, $b$-metric
Received by editor(s): April 15, 1999
Published electronically: August 28, 2000
Communicated by: Józef Dodziuk
Article copyright: © Copyright 2000 M. S. Joshi