In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over...In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.展开更多
Two alternate arguments in the framework of intrinsic metrics and measures respectively of part of the proof of a famous theorem due to Qi-Keng Lu on Bergman metric with constant negative holomorphic sectional curvatu...Two alternate arguments in the framework of intrinsic metrics and measures respectively of part of the proof of a famous theorem due to Qi-Keng Lu on Bergman metric with constant negative holomorphic sectional curvature are presented.A relationship between the Lu constant and the holo- morphic sectional curvature of the Bergman metric is given.Some recent progress of the Yau’s porblem on the characterization of domain of holomorphy on which the Bergman metric is K(?)hler-Einstein is described.展开更多
In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows： Let D be a smoothly bounded domain in Cn. Suppose...In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows： Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} C Aut（D） such that {gj（z）} accumulates at a boundary point p ∈δD for some z C D. Then DD is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture： Let D be a bounded convex domain in C2 with C2 boundary. Suppose that there is a sequence {gj} Aut（D） such that {gj（z）} accumulates at a boundary point for some point z ∈ D. Then if p E OD is such an orbit accumulation point, OD contains no non-trivial analytic variety passing through p.展开更多
文摘In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.
基金This work was partially supported by Research Grants Council of the Hong Kong SAR,China(Grant No.HKUT017/05P)
文摘Two alternate arguments in the framework of intrinsic metrics and measures respectively of part of the proof of a famous theorem due to Qi-Keng Lu on Bergman metric with constant negative holomorphic sectional curvature are presented.A relationship between the Lu constant and the holo- morphic sectional curvature of the Bergman metric is given.Some recent progress of the Yau’s porblem on the characterization of domain of holomorphy on which the Bergman metric is K(?)hler-Einstein is described.
文摘In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows： Let D be a smoothly bounded domain in Cn. Suppose there exists {gj} C Aut（D） such that {gj（z）} accumulates at a boundary point p ∈δD for some z C D. Then DD is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture： Let D be a bounded convex domain in C2 with C2 boundary. Suppose that there is a sequence {gj} Aut（D） such that {gj（z）} accumulates at a boundary point for some point z ∈ D. Then if p E OD is such an orbit accumulation point, OD contains no non-trivial analytic variety passing through p.
