We study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant.For a static vacuum(Mn,g,V),we also compute the asymptotic expansions of g and V at conformal infinity.
The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.
We define a class of geometric flows on a complete Kahler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equa- tions, derivative nonlinear SchrSdinger equations etc. Furthermore, we consider the existence for these flows from S1 into a complete Kahler manifold and prove some local and global existence results.
We define a kind of KdV （Korteweg-de Vries） geometric flow for maps from a real line or a circle into a Kahler manifold （N,J,h） with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.
In this paper,a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized（third order） Landau-Lifshitz equation. On the other hand it could be thought of as a special case of the Schroodinger-Airy flow when the target manifold is a Koahler manifold with constant holomorphic sectional curvature. We show the local existence of the new flow on a complete Riemannian manifold with some assumptions on Ricci tensor. Moreover,if the target manifolds are Einstein or some certain type of locally symmetric spaces,the global results are obtained.
