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Sparse Beltrami Coefficients, Integral Means of Conformal Mappings and the Feynman-Kac Formula

Ivrii, Oleg (2018) Sparse Beltrami Coefficients, Integral Means of Conformal Mappings and the Feynman-Kac Formula. Potential Analysis, 48 (4). pp. 437-457. ISSN 0926-2601. doi:10.1007/s11118-017-9642-x. https://resolver.caltech.edu/CaltechAUTHORS:20170706-154349614

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Abstract

In this note, we give an estimate for the dimension of the image of the unit circle under a quasiconformal mapping whose dilatation has small support. We also prove an analogous estimate for the rate of growth of a solution of a second-order parabolic equation given by the Feynman-Kac formula with a sparsely supported potential and introduce a dictionary between the two settings.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1007/s11118-017-9642-xDOIArticle
https://rdcu.be/MFdyPublisherFree ReadCube access
https://arxiv.org/abs/1608.05872arXivDiscussion Paper
Additional Information:© 2017 Springer Science+Business Media B.V. Received: 04 January 2017; Accepted: 28 June 2017; First Online: 04 July 2017. The author wishes to thank Kari Astala, Ilia Binder, István Prause and Eero Saksman for interesting conversations and the anonymous referee for a number of corrections and helpful suggestions. The research was funded by the Academy of Finland, project nos. 271983 and 273458.
Funders:
Funding AgencyGrant Number
Academy of Finland271983
Academy of Finland273458
Subject Keywords:Conformal mapping; Integral means spectrum; Quasiconformal extension; Hyperbolic Brownian motion; Feynman-Kac formula
Issue or Number:4
Classification Code:Mathematics Subject Classification (2010): 30C75; 30D45; 31A15
DOI:10.1007/s11118-017-9642-x
Record Number:CaltechAUTHORS:20170706-154349614
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170706-154349614
Official Citation:Ivrii, O. Potential Anal (2018) 48: 437. https://doi.org/10.1007/s11118-017-9642-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78823
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Jul 2017 22:54
Last Modified:15 Nov 2021 17:43

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