@article{e4bdad76bb054b32bce728895c33995b,
title = "Steklov Eigenvalues and Quasiconformal Maps of Simply Connected Planar Domains",
abstract = "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.",
author = "A. Girouard and Laugesen, {R. S.} and Siudeja, {B. A.}",
note = "This work was partially supported by grants from the FRQNT New Researchers Start-up Program (to Alexandre Girouard), Simons Foundation (#204296 to Richard Laugesen), National Science Foundation grant DMS-0803120, University of Illinois Research Board, and Polish National Science Centre (2012/07/B/ST1/03356 to Bart?omiej Siudeja). We are grateful to the following research centers for supporting our participation in workshops at which this paper was developed: MFO-Oberwolfach ?Geometric Aspects of Spectral Theory? (July 2012); de Giorgi Center at the Scuola Normale in Pisa ?New Trends in Shape Optimization? (July 2012); Universit? de Neuch?tel ?Workshop on Spectral Theory and Geometry? (June 2013); Banff International Research Station ?Spectral Theory of Laplace and Schr?dinger Operators? (July 2013).",
year = "2016",
month = feb,
day = "1",
doi = "10.1007/s00205-015-0912-8",
language = "English (US)",
volume = "219",
pages = "903--936",
journal = "Archive for Rational Mechanics and Analysis",
issn = "0003-9527",
publisher = "Springer New York",
number = "2",
}