In this paper we investigate an overdetermined system of differential equations, which is a generalization of both the Cauchy-Riemann equations and the Beltrami equation. The conditions under which the Neumann problem...In this paper we investigate an overdetermined system of differential equations, which is a generalization of both the Cauchy-Riemann equations and the Beltrami equation. The conditions under which the Neumann problem for the overdetermined system can be solved are given.展开更多
The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context...The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D'Angelo concerning the ineffectiveness of the latter.(ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations.(iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.展开更多
The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algeb...The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.展开更多
基金Prcject supported by the National Natural science Foundation of China
文摘In this paper we investigate an overdetermined system of differential equations, which is a generalization of both the Cauchy-Riemann equations and the Beltrami equation. The conditions under which the Neumann problem for the overdetermined system can be solved are given.
文摘The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D'Angelo concerning the ineffectiveness of the latter.(ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations.(iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.
基金supported by a grant from the National Science Foundation.
文摘The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.
