Quasi-invariance of Brownian measures on the group of circle homeomorphisms and infinite-dimensional Riemannian geometry

Airault, 1999, The Heisenberg group H3 in terms of the orthonormal frame bundle O(R2) and the control of variation of the Heisenberg diffusion, 23 Airault, 2005, Riemannian connections and curvatures on the universal Teichmuller space, C. R. Math. Acad. Sci. Paris, 341, 353, 10.1016/j.crma.2005.06.028 Airault, 2003, Realization of Virasoro unitarizing measures on the set of Jordan curves, C. R. Math. Acad. Sci. Paris, 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, 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 Airault, 2002, Support of Virasoro unitarizing measures, C. R. Math. Acad. Sci. Paris, 335, 621, 10.1016/S1631-073X(02)02539-6 Airault, 2004, Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows, J. Math. Pures Appl., 83, 955, 10.1016/j.matpur.2004.06.001 Beurling, 1959, Espaces de Dirichlet I. Le cas élémentaire, Acta Math., 99, 203, 10.1007/BF02392426 Bismut, 1984 Bowick, 1988, The Ricci curvature of Diff(S1)/SL(2,R), J. Math. Phys., 29, 1979, 10.1063/1.527854 Bowick, 1987, String theory as the Kähler geometry of loop space, Phys. Rev. Lett., 58, 535, 10.1103/PhysRevLett.58.535 Bowick, 1987, The holomorphic geometry of closed bosonic string theory and Diff(S1)/S1, Nuclear Phys. B, 293, 348, 10.1016/0550-3213(87)90076-9 Cruzeiro, 1996, Renormalized differential geometry on path space: Structural equation, curvature, J. Funct. Anal., 139, 119, 10.1006/jfan.1996.0081 Driver, 1992, A Cameron–Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, J. Funct. Anal., 110, 272, 10.1016/0022-1236(92)90035-H Driver, 1997, Integration by parts and quasi-invariance for heat kernel measures on loop groups, J. Funct. Anal., 149, 470, 10.1006/jfan.1997.3103 Fang, 1999, Integration by parts for heat measures over loop groups, J. Math. Pures Appl., 78, 877, 10.1016/S0021-7824(99)00133-6 Fang, 2002, Canonical Brownian motion on the diffeomorphism group of the circle, J. Funct. Anal., 196, 162, 10.1006/jfan.2002.3922 Fang, 1993, Stochastic analysis on the path space of a Riemannian manifold, J. Funct. Anal., 118, 249, 10.1006/jfan.1993.1145 M. Gordina, P. Lescot, Riemannian geometry on Diff(S1)/S2, J. Funct. Anal., in press Hong, 1991, Universal Teichmüller space and DiffS1/S1, Comm. Math. Phys., 135, 401, 10.1007/BF02098049 Kirillov, 1998, Geometric approach to discrete series of unireps for Vir, J. Math. Pures Appl., 77, 746, 10.1016/S0021-7824(98)80007-X Kirillov, 1986, Kähler geometry of the infinite-dimensional homogeneous space M=Diff+(S1)/Rot(S1), Funktsional. Anal. i Prilozhen., 20, 79 Kunita, 1991 Kunita, 1967, L2-martingales, Nagoya J. Math., 30, 209, 10.1017/S0027763000012484 Le Jan, 2002, Integration of Brownian fields, Ann. Probab., 30, 826, 10.1214/aop/1023481009 Neretin, 1994, Some remarks on quasi-invariant actions of loop groups and the group of diffeomorphisms of the circle, Comm. Math. Phys., 164, 599, 10.1007/BF02101492