Fredholm, Hodge and Liouville theorems on noncompact manifolds

Lockhart, Robert

doi:10.1090/S0002-9947-1987-0879560-0

Fredholm, Hodge and Liouville theorems on noncompact manifolds

Author: Robert Lockhart
Journal: Trans. Amer. Math. Soc. 301 (1987), 1-35
MSC: Primary 58G30; Secondary 47B38, 58A12
DOI: https://doi.org/10.1090/S0002-9947-1987-0879560-0
MathSciNet review: 879560
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Abstract: Fredholm, Liouville, Hodge, and ${L^2}$ -cohomology theorems are proved for Laplacians associated with a class of metrics defined on manifolds that have finitely many ends. The metrics are conformal to ones that are asymptotically translation invariant. They are not necessarily complete. The Fredholm results are, of necessity, with respect to weighted Sobolev spaces. Embedding and compact embedding theorems are also proved for these spaces.

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