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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.

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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.

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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.
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
Record Number:CaltechAUTHORS:20170706-154349614
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Official Citation:Ivrii, O. Potential Anal (2018) 48: 437.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78823
Deposited By: Tony Diaz
Deposited On:06 Jul 2017 22:54
Last Modified:15 Nov 2021 17:43

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