A homotopy formula for a loced q-concave wedge in Stein manifolds is obtained, by using this formula the -equation on local q-concave wedges is solved, and an extension problem on local q-concave wedges is discussed.
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
A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman...A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula without boundary integral of (r, s) differential forms, which is different from the classical one. The new weighted formula is especially suitable for the case of the local g-concave wedge with a non-smooth boundary, so one can avoid complex estimates of boundary integrals and the density of integral may be not defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the interpolation of functions.展开更多
In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^...In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},展开更多
We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Dona...We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Donaldson's lower bound for the L^2-norm of the Hermitian scalar curvature.展开更多
文摘A homotopy formula for a loced q-concave wedge in Stein manifolds is obtained, by using this formula the -equation on local q-concave wedges is solved, and an extension problem on local q-concave wedges is discussed.
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National Natural Science Foundation and Mathematical "Tian Yuan" Foundation of China (10271097 and TY10126033)
文摘A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula without boundary integral of (r, s) differential forms, which is different from the classical one. The new weighted formula is especially suitable for the case of the local g-concave wedge with a non-smooth boundary, so one can avoid complex estimates of boundary integrals and the density of integral may be not defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the interpolation of functions.
基金Project supported by the National Natural Science Foundation of China
文摘In this article we always assume r+q≤n, otherwise the result is trivial. Now we introduce some definitions and notations.Definition 1. Suppose D is a connected open subset in an n-dimensional complex manifold with C^2-boundary. We say function φ is a defining function of if there exists an open neighborhood U of x such that φ: U→R and D ∩ U={y∈M|φ(y)【0},
基金supported by National Natural Science Foundation of China(Grant Nos.11401232 and 11528103)Agence nationale de la recherche(Grant No.ANR-14-CE25-0012-01)funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative and Deutsche Forschungsgemeinschaft Funded Project Sonderforschungsbereich Transregio 191
文摘We prove an estimate for Donaldson's Q-operator on a prequantized compact symplectic manifold.This estimate is an ingredient in the recent result of Keller and Lejmi(2017) about a symplectic generalization of Donaldson's lower bound for the L^2-norm of the Hermitian scalar curvature.
