Advanced Studies in Pure Mathematics

Behavior of Eigenfunctions near the Ideal Boundary of Hyperbolic Space

Harold Donnelly

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Abstract

The spectrum of the Laplacian on hyperbolic space is a proper subset of the positive reals. We study eigenfunctions, defined on the complements of compact sets, whose eigenvalues lie below the bottom of the spectrum. Such eigenfunctions may arise by perturbing the metric on compact subsets of the space. One divides the eigenfunctions by normalizing factors, so that the quotients have analytic boundary values on the ideal boundary at infinity. The renormalized eigenfunctions are approximated by special polynomials, in nontangential approach regions to the ideal boundary.

Article information

Source
Minimal Surfaces, Geometric Analysis and Symplectic Geometry, K. Fukaya, S. Nishikawa and J. Spruck, eds. (Tokyo: Mathematical Society of Japan, 2002), 15-29

Dates
First available in Project Euclid: 31 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546230291

Digital Object Identifier
doi:10.2969/aspm/03410015

Mathematical Reviews number (MathSciNet)
MR1925733

Zentralblatt MATH identifier
1035.58019

Subjects
Primary: 58G25

Citation

Donnelly, Harold. Behavior of Eigenfunctions near the Ideal Boundary of Hyperbolic Space. Minimal Surfaces, Geometric Analysis and Symplectic Geometry, 15--29, Mathematical Society of Japan, Tokyo, Japan, 2002. doi:10.2969/aspm/03410015. https://projecteuclid.org/euclid.aspm/1546230291


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