In this paper, a result on the persistence of lower dimensional invariant tori in C d reversible systems is obtained under some conditions. The theorem is proved for any d which is larger than some constants.
Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.
Concerning a bounded sequence of finite energy weak solutions to the compressible Navier-Stokes-Poisson system (denoted by CNSP), which converges up to extraction of a subsequence, the limit system may not be the same system. By introducing Young measures as in [6, 15], the authors deduce the system (HCNSP) which the limit functions must satisfy. Then they solve this system in a subclass where Young measures are convex combinations of Dirac measures, to give the information on the propagation of density-oscillations. The results for strong solutions to (CNSP) (see Corollary 6.1) are also obtained.
In this article, some uniqueness theorems of meromorphic mappings in several complex variables sharing hyperplanes in general position are proved with truncated multiplicities.
The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Kähler-Ricci flow. The positivity of Ricci curvature is also preserved along the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Kähler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Kähler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.
The authors discuss the proper holomorphic mappings between special Hartogs triangles of different dimensions and obtain a corresponding classification theorem.
The author obtains some weighted Hardy-type inequalities on H-type groups and anisotropic Heisenberg groups. These inequalities generalize some recent results due to N. Garofalo, E. Lanconelli, I. Kombe and P. Niu et al.
The author proves that the right-hand term of a p-Laplace equation is zero on the singular set of a local solution to the equation. Such a result is used to study the existence of an optimal control problem.