Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake
Dynamical Systems
2024-01-29 v2 Classical Analysis and ODEs
Metric Geometry
Abstract
We apply recent results by the authors to obtain bounds on remainder terms of the Dirichlet Laplace eigenvalue counting function for domains that can be realised as countable disjoint unions of scaled Koch snowflakes. Moreover we compare the resulting exponents to the exponents in the asymptotic expansion of the domain's inner parallel volume.
Keywords
Cite
@article{arxiv.2312.12331,
title = {Eigenvalue counting functions and parallel volumes for examples of fractal sprays generated by the Koch snowflake},
author = {Sabrina Kombrink and Lucas Schmidt},
journal= {arXiv preprint arXiv:2312.12331},
year = {2024}
}
Comments
Added details, fixed typos. 15 pages, 10 figures