首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Estimates for the -Neumann problem and nonexistence of C 2 Levi-flat hypersurfaces in
Authors:Jianguo Cao  Mei-Chi Shaw  Lihe Wang
Institution:(1) Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA;(2) Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Abstract:Let OHgr be a pseudoconvex domain with C2 boundary in MediaObjects/s00209-004-0661-0flb3.gif, n ge 2. We prove that the MediaObjects/s00209-004-0661-0flb4.gif-Neumann operator N exists for square-integrable forms on OHgr. Furthermore, there exists a number epsi0>0 such that the operators MediaObjects/s00209-004-0661-0flb5.gif and the Bergman projection are regular in the Sobolev space Wepsi ( OHgr) for epsi<epsi0. The MediaObjects/s00209-004-0661-0flb4.gif-Neumann operator is used to construct MediaObjects/s00209-004-0661-0flb4.gif-closed extension on OHgr for forms on the boundary bOHgr. This gives solvability for the tangential Cauchy-Riemann operators on the boundary. Using these results, we show that there exist no non-zero L2-holomorphic (p, 0)-forms on any domain with C2 pseudoconcave boundary in MediaObjects/s00209-004-0661-0flb3.gif with p > 0 and n ge 2. As a consequence, we prove the nonexistence of C2 Levi-flat hypersurfaces in MediaObjects/s00209-004-0661-0flb3.gif.This paper is a revision of our preprint (May 2003) formerly titled ldquoEstimates for the MediaObjects/s00209-004-0661-0flb4.gif-Neumann problem and nonexistence of Levi-flat hypersurfaces in MediaObjects/s00209-004-0661-0flb3.gifrdquo where the nonexistence of C2,agr Levi-flat hypersurfaces is proved for agr>0.All three authors are partially supported by NSF grants.An erratum to this article can be found at
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号