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Published May 2018 | Submitted
Journal Article Open

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

Ivrii, Oleg

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.

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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