this paper,the authors introduce a Morse-theoretic condition under which the Levi form is allowed to have negative eigenvalues outside critical locus,and show that the existence of an exhaustion function satisfying su...this paper,the authors introduce a Morse-theoretic condition under which the Levi form is allowed to have negative eigenvalues outside critical locus,and show that the existence of an exhaustion function satisfying such a condition leads to vanishing theorems.展开更多
A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the sol...A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of -equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.展开更多
In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality ...In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12431005,12571086).
文摘this paper,the authors introduce a Morse-theoretic condition under which the Levi form is allowed to have negative eigenvalues outside critical locus,and show that the existence of an exhaustion function satisfying such a condition leads to vanishing theorems.
基金Supported by the National Natural Science Foundation and Mathematical "Tian Yuan" Foundation of China and the Natural Science Foundation of Fujian (Grant No. 10271097, TY10126033, F0110012)
文摘A new Koppelman-Leray-Norguet formula of (p,q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein manifold is obtained, and an integral representation for the solution of -equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.
基金supported by the Korea Research Foundation Grant funded by Korea Government(MOEHRD,Basic Research Promotion Fund)(Grant No.KRF-2005-070-C00007)
文摘In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.
