Fractional Laplacian in conformal geometry

Andersson, 1992, On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations, Comm. Math. Phys., 149, 587, 10.1007/BF02096944

Aviles, 1988, Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds, Duke Math. J., 56, 395, 10.1215/S0012-7094-88-05616-5

X. Cabré, Y. Sire, Non-linear equations for fractional Laplacians I: regularity, maximum principles and Hamiltonian estimates, in preparation.

L.A. Caffarelli, J.-M. Roquejoffre, O. Savin, Non-local minimal surfaces, in press.

Caffarelli, 2008, Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian, Invent. Math., 171, 425, 10.1007/s00222-007-0086-6

Caffarelli, 2007, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32, 1245, 10.1080/03605300600987306

L.A. Caffarelli, P.E. Souganidis, Convergence of nonlocal threshold dynamics approximations to front propagation, preprint, 2008.

L.A. Caffarelli, E. Valdinoci, Regularity properties of nonlocal minimal surfaces via limiting arguments, preprint, 2009.

L.A. Caffarelli, A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, Ann. of Math., in press.

Fabes, 1982, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations, 7, 77, 10.1080/03605308208820218

C. Fefferman, C.R. Graham, The ambient metric, in press.

M.d.M. González, R. Mazzeo, Y. Sire, Singular solutions of fractional order conformal Laplacians (2009), submitted for publication.

M.d.M. González, J. Qing, Some results on the fractional Yamabe problem, in preparation.

Graham, 2000, Volume and area renormalizations for conformally compact Einstein metrics, vol. 63, 31

Graham, 1992, Conformally invariant powers of the Laplacian. I. Existence, J. Lond. Math. Soc. (2), 46, 557, 10.1112/jlms/s2-46.3.557

Graham, 1991, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math., 87, 186, 10.1016/0001-8708(91)90071-E

Graham, 2003, Scattering matrix in conformal geometry, Invent. Math., 152, 89, 10.1007/s00222-002-0268-1

Guillarmou, 2005, Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds, Duke Math. J., 129, 1, 10.1215/S0012-7094-04-12911-2

Guillarmou, 2007, The determinant of the Dirichlet-to-Neumann map for surfaces with boundary, Int. Math. Res. Not. IMRN, 26

C. Guillarmou, J. Qing, Spectral characterization of Poincaré–Einstein manifolds with infinity of positive Yamabe type, preprint, 2009.

Mazzeo, 1991, Regularity for the singular Yamabe problem, Indiana Univ. Math. J., 40, 1277, 10.1512/iumj.1991.40.40057

Mazzeo, 1987, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal., 75, 260, 10.1016/0022-1236(87)90097-8

Muckenhoupt, 1972, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc., 165, 207, 10.1090/S0002-9947-1972-0293384-6

Paneitz, 2008, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (summary), SIGMA Symmetry Integrability Geom. Methods Appl., 4

Peterson, 2000, Conformally covariant pseudo-differential operators, Differential Geom. Appl., 13, 197, 10.1016/S0926-2245(00)00023-1

Qing, 2006, On positive solutions to semilinear conformally invariant equations on locally conformally flat manifolds, Int. Math. Res. Not., 20