Manifolds whose Weyl spectral asymptotics have small but not tiny remainders
Michael Taylor
University of North Carolina at Chapel Hill, Chapel Hill, USA
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Abstract
A compact, -dimensional Riemannian manifold has Weyl spectral asymptotics with remainder ; i.e., the spectral counting function satisfies , with . Generally, one actually has , and one seeks geometrical conditions under which stronger estimates hold on the remainder and also conditions limiting how extra small the remainder can be. Here, we produce -dimensional manifolds whose Weyl remainders are but not for any .
Cite this article
Michael Taylor, Manifolds whose Weyl spectral asymptotics have small but not tiny remainders. J. Spectr. Theory 14 (2024), no. 2, pp. 697–717
DOI 10.4171/JST/510