# Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains

```@article{Girouard2014SteklovEA,
title={Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains},
author={Alexandre Girouard and Richard S. Laugesen and Bartlomiej A. Siudeja},
journal={Archive for Rational Mechanics and Analysis},
year={2014},
volume={219},
pages={903-936}
}```
• Published 2014
• Mathematics
• Archive for Rational Mechanics and Analysis
We investigate isoperimetric upper bounds for sums of consecutive Steklov eigenvalues of planar domains. The normalization involves the perimeter and scale-invariant geometric factors which measure deviation of the domain from roundness. We prove sharp upper bounds for both starlike and simply connected domains for a large collection of spectral functionals including partial sums of the zeta function and heat trace. The proofs rely on a special class of quasiconformal mappings.
15 Citations

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