Acta mathematica scientia, Series B >
SOLVING ∂b ON PARABOLIC LAMINATIONS
Received date: 2013-08-02
Revised date: 2014-06-09
Online published: 2014-11-20
Supported by
Supported by the National Natural Science Foundation of China (11271359).
Let X be a compact set which is laminated by parabolic Riemiann surfaces. For the CR positive line bundle L, there exists an integer N ∈ N such that for any s > N and any continuous v ∈∧(0,1) XLs, there exists a continuous u ∈Ls solving ∂bu = v.
Key words： parabolic; affine continuous; Riemann surface lamination; ∂-equation
WANG Gang . SOLVING ∂b ON PARABOLIC LAMINATIONS[J]. Acta mathematica scientia, Series B, 2014 , 34(6) : 1811 -1825 . DOI: 10.1016/S0252-9602(14)60125-9
[1] H¨ormander L. L2 estimates and existence theorems for the ¯@ operator. Acta Math, 1965, 113: 89–152
[2] Fornæss J E, Wold E F. Solving ∂b on hyperbolic laminations. http://arxiv.org/pdf/1108.2286
[3] Dinh T C, Nguyˆen V A, Sibony N. Heat equation and ergodic theorems for Riemann surface laminations. Ann Math, 2012, 354: 331–376
[4] Fornæss J E, Sibony N. Riemann surface laminations with singularities. J Geom Anal, 2008, 18(2): 400–422
[5] Candel A, Conlon L. Foliations I. Providence, RI: American Mathematical Society, 1999
[6] Demailly J P. Complex analytic and algebraic geometry. http://www-fourier.ujf-grenoble.fr/ demailly/
[7] Berndtsson B, Sibony N. The ∂-equation on a positive current. Invent Math, 2002, 147(2): 371–428
[8] Candel A. Uniformization of surface laminations. Ann Sci ´Ecole Norm Sup, 1993, 26(4): 489–516
[9] Chai X. Properties of solutions of differential equations on laminations. REU Project at the University of Michigan, 2010
[10] Glutsuk A A. Smoothness of the uniformization of two-dimensional linear foliation on torus with nonstandard metric. http://arxiv.org/pdf/9911154v2
[11] Ghys E. sur l’uniformisation des lamiantions paraboliques//Albert C, Brouzet R, Dufour J P, eds. Integrable
Systems and Foliations. Boston: Birkh¨auser Boston, 1997: 73–91
[12] Fornæss J E, Sibony N, Wold E F. Examples of minimal lamination and associated currents. Math Zeit, 2011, 269: 495–520
/
| 〈 |
|
〉 |