A model form for exact $b$-metrics
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- by M. S. Joshi PDF
- Proc. Amer. Math. Soc. 129 (2001), 581-584
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
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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
- Received by editor(s): April 15, 1999
- Published electronically: August 28, 2000
- Communicated by: Józef Dodziuk
- © Copyright 2000 M. S. Joshi
- Journal: Proc. Amer. Math. Soc. 129 (2001), 581-584
- MSC (2000): Primary 58J50
- DOI: https://doi.org/10.1090/S0002-9939-00-05599-4
- MathSciNet review: 1707151