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 | ||||||||||||
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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. | ||||||||||||
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| 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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