The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting; theorem is generalized. They also stu...The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting; theorem is generalized. They also study topology of such manifolds.展开更多
In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat b...In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat boundary in complex manifolds.展开更多
文摘The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting; theorem is generalized. They also study topology of such manifolds.
基金supported by NSF(Grant No.DMS 1500952)supported by NSF(Grant No.DMS 1700003)
文摘In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat boundary in complex manifolds.
