Limiting absorption principle on manifolds having ends with various measure growth rate limits | Zendy

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Limiting absorption principle on manifolds having ends with various measure growth rate limits

Author(s) -

Kumura Hironori

Publication year - 2013

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/pds057

Subject(s) - mathematics , limiting , mathematical analysis , limit (mathematics) , riemannian manifold , laplace–beltrami operator , measure (data warehouse) , resolvent , infinity , operator (biology) , laplace operator , manifold (fluid mechanics) , pure mathematics , p laplacian , mechanical engineering , biochemistry , chemistry , repressor , database , computer science , transcription factor , engineering , gene , boundary value problem

The purpose of this paper is to discuss the properties of the resolvent of the Laplace–Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which has a different limit of the growth rate of the Riemannian measure at infinity, in particular, focusing on the limiting absorption principle. As a result, we will obtain the absolute continuity of the Laplace–Beltrami operator.

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