Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows

Ahlfors, 1966, Lectures on Quasiconformal Mappings, vol. 10 Airault, 2003, Realization of Virasoro unitarizing measures on the set of Jordan curves, C. R. Acad. Sci. Paris, Sér. I, 336, 429, 10.1016/S1631-073X(03)00085-2 Airault, 2001, Unitarizing probability measures for representations of Virasoro algebra, J. Math. Pures Appl., 80, 627, 10.1016/S0021-7824(01)01220-X Airault, 2002, Support of Virasoro unitarizing measures, C. R. Math. Acad. Sci. Paris, Sér. I, 335, 621, 10.1016/S1631-073X(02)02539-6 Airault, 2002, Modulus of continuity of the canonic Brownian motion “on the group of diffeomorphisms of the circle”, J. Funct. Anal., 196, 395, 10.1016/S0022-1236(02)00011-3 Beurling, 1956, The boundary correspondence under quasiconformal mappings, Acta Math., 96, 125, 10.1007/BF02392360 Cao, 2003, On a type of stochastic differential equations driven by countably many Brownian motions, J. Funct. Anal., 203, 262, 10.1016/S0022-1236(03)00066-1 Caratheodory, 1913, Über die gegenseitige Beziehung der Ränder bei der konformen Abbildung des Inneren einer Jordanschen Kurve auf einen Kreis, Math. Ann., 75, 305, 10.1007/BF01456720 Fang, 2002, Canonical Brownian motion on the diffeomorphism group of the circle, J. Funct. Anal., 196, 162, 10.1006/jfan.2002.3922 Fang, 2003, A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion, C. R. Acad. Sci. Paris, 337, 737, 10.1016/j.crma.2003.10.008 Hamilton, 1991, Generalized conformal welding, Ann. Acad. Sci. Fenn. Ser. A I Math., 16, 333, 10.5186/aasfm.1991.1610 Ikeda, 1977, A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math., 14, 619 Ikeda, 1989, Stochastic Differential Equations and Diffusion Processes, vol. 24 Iwaniec, 2002, Spectral Methods of Automorphic Forms, vol. 53 Jones, 2000, Removability theorems for Sobolev functions and quasiconformal maps, Ark. Mat., 38, 263, 10.1007/BF02384320 Katznelson, 1990, On conformal welding homeomorphisms associated to Jordan curves, Ann. Acad. Sci. Fenn. Ser. A I Math., 15, 293, 10.5186/aasfm.1990.1517 Kirillov, 1998, Geometric approach to discrete series of unirreps for Virasoro, J. Math. Pures Appl., 77, 735, 10.1016/S0021-7824(98)80007-X Kunita, 1990, Stochastic Flows and Stochastic Differential Equations, vol. 24 Lawler, 2002, Analyticity of intersection exponents for planar Brownian motion, Acta Math., 189, 179, 10.1007/BF02392842 Le Jan, 2002, Integration of Brownian vector fields, Ann. Probab., 30, 826, 10.1214/aop/1023481009 Lehto, 1987, Univalent Functions and Teichmüller Spaces, vol. 109 Malliavin, 1997, Stochastic Analysis, vol. 313 Malliavin, 1999, The canonic diffusion above the diffeomorphism group of the circle, C. R. Acad. Sci. Paris, Sér. I, 329, 325, 10.1016/S0764-4442(00)88575-4 McKean, 1969, Stochastic Integrals, vol. 5 Pommerenke, 1992, Boundary Behaviour of Conformal Maps, vol. 299 Ren, 2003, Stochastic flow for SDEs with non-Lipschitz coefficients, Bull. Sci. Math., 127, 739, 10.1016/S0007-4497(03)00062-9