The equation on weakly pseudo-convex CR manifolds of dimension 3 |
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Authors: | Joseph J Kohn Andreea C Nicoara |
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Institution: | aDepartment of Mathematics, Princeton University, Princeton, NJ 08544-1000, USA;bDepartment of Mathematics, Harvard University, 1 Oxford St., Cambridge, MA 02138, USA |
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Abstract: | Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of dimension 3, embedded in (N2), of codimension one or more, and endowed with the induced CR structure. Assuming that the tangential Cauchy-Riemann operator has closed range in L2(M) in order to rule out the Rossi example, we push regularity up to show has closed range in Hs(M) for all s>0. We then use the Szegö projection to show there is a smooth solution for the problem given smooth data. The results are obtained via microlocalization by piecing together estimates for functions and (0,1) forms that hold on different microlocal regions. |
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Keywords: | Embedded CR manifold closed range of sciencedirect " target="_blank">com/cache/MiamiImageURL/B6WJJ-4HH81VN-1-3/0?wchp=dGLbVzz-zSkzk" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=20 width="15"/> microlocalization |
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