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Global Analysis on Open Manifolds

Jürgen Eichhorn

出版	Nova Publishers, 2007
主題	Mathematics / Geometry / GeneralScience / Physics / Mathematical & Computational
ISBN	16002156379781600215636
URL	http://books.google.com.hk/books?id=JgiCtfP_cz4C&hl=&source=gbs_api
EBook	SAMPLE

註釋

Global analysis is the analysis on manifolds. Since the middle of the sixties there exists a highly elaborated setting if the underlying manifold is compact, evidence of which can be found in index theory, spectral geometry, the theory of harmonic maps, many applications to mathematical physics on closed manifolds like gauge theory, Seiberg-Witten theory, etc. If the underlying manifold is open, i.e. non-compact and without boundary, then most of the foundations and of the great achievements fail. Elliptic operators are no longer Fredholm, the analytical and topological indexes are not defined, the spectrum of self-adjoint elliptic operators is no longer discrete, functional spaces strongly depend on the operators involved and the data from geometry, many embedding and module structure theorems do not hold, manifolds of maps are not defined, etc. It is the goal of this new book to provide serious foundations for global analysis on open manifolds, to discuss the difficulties and special features which come from the openness and to establish many results and applications on this basis.