The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as th...The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.展开更多
The homogeneous quadratic riemann boundary value problem (1) with H?lder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its gene...The homogeneous quadratic riemann boundary value problem (1) with H?lder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained. Key words homogeneous quadratic Riemann boundary value problem - ordinary and special nodes - index - sectionally holomorphic function CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19871064)Biography: Lu Jian-ke (1922-), male, Professor, research direction: complex analysis and its applications.展开更多
Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comp...Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.展开更多
Let YIV be the Super-Cartan domain of the fourth type, We reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X（Z, W）. This differential equation can be...Let YIV be the Super-Cartan domain of the fourth type, We reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X（Z, W）. This differential equation can be solved to give an implicit function in X. We give the generating function of the Einstein Kahler metric on YIV. We obtain the explicit form of the complete Einstein-Kahler metric on YIV for a special case.展开更多
基金Supported by the National Natural Science Foundation of China !(No.19871064)
文摘The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.
文摘The homogeneous quadratic riemann boundary value problem (1) with H?lder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained. Key words homogeneous quadratic Riemann boundary value problem - ordinary and special nodes - index - sectionally holomorphic function CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19871064)Biography: Lu Jian-ke (1922-), male, Professor, research direction: complex analysis and its applications.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10071051 and 10171068)Natural Science Foundation of Beijing(Grant Nos.1002004 and 1012004).
文摘Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.
基金Supported by National Natural Science Foundation of China(Grant No.10471097)Scientific Research Common Program of Beijing Municipal Commission of Education(Grant NO.KM200410028002)Supported by National Natural Science Foundation of China(Grant No
文摘Let YIV be the Super-Cartan domain of the fourth type, We reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X（Z, W）. This differential equation can be solved to give an implicit function in X. We give the generating function of the Einstein Kahler metric on YIV. We obtain the explicit form of the complete Einstein-Kahler metric on YIV for a special case.
