Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007. / Includes bibliographical references (p. 92). / We prove an analogue of the Hodge cohomology theorem for a certain class of non-compact manifolds. Specifically, let M be a compact manifold with boundary OM, and let g be a metric on Int(M). Assume that there exists a collar neighborhood of the boundary ... We then describe doubly weighted Sobolev spaces on M. For elements of these spaces the harmonic parts of w1 and w2 lie in one Sobolev space, while the non-harmonic parts of w1 and w2 lie in a differently defined Sobolev space. We prove that ... is Fredholm on almost all of these doubly weighted spaces, except for a finite number of values of w. This gives us an analogue of the Hodge decomposition theorem and leads to the result. This work generalizes earlier theorems of Atiyah, Patodi and Singer for b-metrics (case a = b = 0) and of Melrose for scattering metrics (case a = b = 1). / by Yakov Shapiro. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/41724 |
| Date | January 2007 |
| Creators | Shapiro, Yakov (Yakov Mikhaylovich) |
| Contributors | Richard B. Melrose., Massachusetts Institute of Technology. Dept. of Mathematics., Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 92 p., application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
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