In this paper, under some growth condition on the volume of a geodesic ball with radiusr, we compute the essential spectrum of some class of Riemannian manifolds with finite volume. This result refines some earlier results of R. Brooks.
LetG be a group andA aG-graded ring. A (graded) idealI ofA is (graded) essential ifI⊃J≠0 wheneverJ is a nonzero (graded) ideal ofA. In this paper we study the relationship between graded essential ideals ofA, essential ideals of the identity componentA e and essential ideals of the smash productA#G *. We apply our results to prime essential rings, irredundant subdirect sums and essentially nilpotent rings.
In the present paper there are given some existence theorems on simultaneous solutions to fixed point and minimax-type inequality problems, hence to fixed point and variational-type inequality problems.
In this paper we define Weyl's transformations on complete Riemannian manifolds and complete Weyl Quantization. We also prove two isomorphism theorems and give a useful trace formula and some other result.
In this paper, we use the deformation method andG-equivariant theory to prove the existence and multiplicity of harmonic maps from an annulus to the unit sphere in? 3 with symmetric boundary value. In particular, we can get infinitely many homotopically different harmonic maps if the boundary value isS 1-equivariant and nonconstant.
In this paper we study the geometrical properties of Grassmannian manifolds constructed in Minkowski space as submanifolds in a certain pseudo-Euclidean space and give a condition that the generalized Gauss map of a spacelike submanifold in Minkowski space is harmonic.
The purpose of this paper is to investigate the structure of the family of projections of analytic mappings between ultrahyperelliptic surfaces (one kind of algeboid surfaces), by introducing the linear differential equation with polynomial coefficients, and to get a generalization of one result of Ozawa's.
This paper applies the methods of Chudnovsky[2], Osgood[4] and Baker[1] to give a simultaneous approximation theorem to the values of exponential function at algebraic points, which slightly sharpens and generalises the results of Chudnovsky[2],[3].
The new bounds of eigenvalues of polyharmonic operators are deduced. This work is a generalization of some kind of estimates of the biharmonic operator.
We consider the simplified one dimensional PDE's governing the carrier flow in semi-conductor devices via the Painlevé analysis approach, and obtain analytic solutions.