Small eigenvalues of geometrically finite manifolds
Tóm tắt
Let M be a complete geometrically finite manifold of bounded negative curvature, infinite volume, and dimension at least 3.We give both a lower bound for the bottom of the spectrum of M and an upper bound for the number of the small eigenvalues of M. These bounds only depend on the dimension, curvature bounds and the volume of the oneneighborhood of the convex core.
Tài liệu tham khảo
citation_journal_title=Duke Math. J.; citation_title=Geometrical finiteness with variable negative curvature; citation_author=B. Bowditch; citation_volume=77; citation_publication_date=1995; citation_pages=229-274; citation_doi=10.1215/S0012-7094-95-07709-6; citation_id=CR1
citation_journal_title=J. Reine Angew. Math.; citation_title=A lower bound on λ0 for geometrically finite hyperbolic n-manifolds; citation_author=M. Burger, R. Canary; citation_volume=454; citation_publication_date=1994; citation_pages=37-57; citation_id=CR2
citation_journal_title=J. Geom. Anal.; citation_title=Tubes and eigenvalues for negatively curved manifolds; citation_author=P. Buser, B. Colbois, J. Dodziuk; citation_volume=3; citation_issue=1; citation_publication_date=1993; citation_pages=1-26; citation_doi=10.1007/BF01895513; citation_id=CR3
citation_journal_title=Comm. Pure Appl. Math.; citation_title=Differential equations on Riemannian manifolds and their geometric applications; citation_author=S.Y. Cheng, S.T. Yau; citation_volume=28; citation_publication_date=1975; citation_pages=333-354; citation_doi=10.1002/cpa.3160280303; citation_id=CR4
citation_journal_title=Inv. Math.; citation_title=Hausdorff dimension of limit sets I; citation_author=K. Corlette; citation_volume=102; citation_publication_date=1990; citation_pages=521-542; citation_doi=10.1007/BF01233439; citation_id=CR5
citation_title=Spectral Theory and Differential Operators; citation_publication_date=1995; citation_id=CR6; citation_author=E.B. Davies; citation_publisher=Cambridge University Press
citation_journal_title=J. Diff. Geo.; citation_title=Lower bounds for λ1 on a finite-volume hyperbolic manifold; citation_author=J. Dodziuk, B. Randol; citation_volume=24; citation_publication_date=1986; citation_pages=133-139; citation_id=CR7
Fissmer, K. and Hamenstädt, U. Spectral convergence of manifold pairs, to appear inComm. Math. Helv.
citation_journal_title=J. Diff. Geom.; citation_title=Geometry of horospheres; citation_author=E. Heintze, H.J. Im Hof; citation_volume=12; citation_publication_date=1977; citation_pages=481-491; citation_id=CR9
citation_journal_title=J. Diff. Geom.; citation_title=Related aspects of positivity in Riemannian geometry; citation_author=D. Sullivan; citation_volume=25; citation_publication_date=1987; citation_pages=327-351; citation_id=CR10