A Transversal Fredholm Property for the ∂̄-neumann Problem on G-bundles
نویسندگان
چکیده
Let M be a strongly pseudoconvex complex manifold which is also the total space of a principal G-bundle with compact base M/G. Assume also thatG acts onM by holomorphic transformations. For such M , we provide a simple condition on forms α sufficient for the regular solvability of u = α and other problems related to the ∂̄-Neumann problem on M . Similar properties are shared by b.
منابع مشابه
The G-fredholm Property of the ∂̄-neumann Problem
Let H1 and H2 be Hilbert spaces and let B(H1,H2) be the space of bounded linear operators A : H1 → H2. An operator A ∈ B(H1,H2) is said to be Fredholm if first, the kernel ofA is finite-dimensional, and second the image ofA is closed and has finite codimension. An application of the open mapping theorem shows that the closedness requirement on the image is redundant. A well-known example of Fre...
متن کاملA COVERING PROPERTY IN PRINCIPAL BUNDLES
Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...
متن کاملA Boundary Meshless Method for Neumann Problem
Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...
متن کاملA Stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind
In the present work, a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind. The solution of the integral equation is described by the Neumann series expansion. Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method. An algorithm is proposed to sim...
متن کاملOn Fredholm Index,transversal Approximations and Quillen’s Geometric Complex Cobordism of Hilbert Manifolds with Some Applications to Flag Varieties of Loop Groups
In [2], by using Fredholm index we developed a version of Quillen’s geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In this work, by using Quinn’s Transversality Theorem [24], it will be shown that this cobordism theory has a...
متن کامل