In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For any compact manifold with boundary and nonnegative scalar curvature, if it is spin and its boundary can be isometrically embedded into Euclidean space as a stric...

We study the behavior of perturbations of small nonlinear Dirac standing waves. We assume that the linear Dirac operator of reference H = Dm + V has only two double eigenvalues and that degeneracies are due to a symmetry of H (theorem of Kramers). In this case, we can build a small 4-dimensional manifold of stationary solutions tangent to the first eigenspace of H . Then we assume that a resona...

In [4J Orlik defined a free cyclic group action on a homotopy sphere constructed as a Brieskorn manifold and proved the following theorem: THEOREM. Every odd-dimensional homotopy sphere that bounds a para-llelizable manifold admits a free Zp-action for each prime p. On the other hand, it was shown ([3J) that there exists a free Zp-action on a 2n-1 dimensional homotopy sphere so that its orbit s...

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semi-linear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. The characterization is expressed in terms of the almost sure long-time behavior of trajectories of the equation in relation to the stati...

Abstract The motion of particles on spherical 1 + 3 dimensional spacetimes can, under some assumptions, be described by the curves a two-dimensional manifold, optical and Jacobi manifolds for null timelike curves, respectively. In this paper ...

Every compact smooth simply connected 3-manifold is a twisted 3-sphere, so every smooth simply connected 3-manifold is diffeomorphic to S.

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1) ; a robust example of such economies is provided . Theorem 2 establishes that the manifold fl of global pseudo-equilibria is a fiber bundle with the topological structure of a oneor two-fold covering space of G k . ", the space of k planes in R", where k is the number of assets in t...

Abstract The first part of this paper is a generalization the Feix–Kaledin theorem on existence hyperkähler metric neighborhood zero section cotangent bundle Kähler manifold. We show that problem constructing structure complex Lagrangian submanifold in holomorphic symplectic manifold reduces to certain deformations structures. recovered from twisted bundle. then every groupoid over compact Pois...