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

Oleg Ivrii

doi:10.1007/s11118-017-9642-x

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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	437-457
Number of pages	21
Journal	Potential Analysis
Volume	48
Issue number	4
DOIs	https://doi.org/10.1007/s11118-017-9642-x
State	Published - 1 May 2018
Externally published	Yes

Keywords

Conformal mapping
Feynman-Kac formula
Hyperbolic Brownian motion
Integral means spectrum
Quasiconformal extension

All Science Journal Classification (ASJC) codes

Analysis

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10.1007/s11118-017-9642-x

Cite this

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AB - 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.

KW - Conformal mapping

KW - Feynman-Kac formula

KW - Hyperbolic Brownian motion

KW - Integral means spectrum

KW - Quasiconformal extension

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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