Eigenvalue Asymptotics of the Neumann Laplacian of Regions and Manifolds with Cusps
نویسنده
چکیده
We study the eigenvalue asymptotics of a Neumann Laplacian-A$ in unbounded regions 0 of R2 with cusps at infinity (a typical example is a={(~, y)~R~:x>l, Iyl-ce-" I}) and prove that NE(A:)-NE(HY)+ E/2 Vol(Q), where HV is the canonical one-dimensional Schrodinger operator associated to the problem. We establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a Dirichlet Laplacian-A: for a class of cusp-type regions of infinite volume. e 1992 Academic Press, Inc.
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