I. Introduction. Stokes' theorem on a manifold is a central theorem of mathematics. Special cases include the integral theorems of vector analysis and the Cauchy-Goursat theorem. My purpose here is to prove this version of Stokes' Theorem. Let ω be a continuous differential (n − 1)-form on a compact oriented n-manifold M with boundary ∂M. Suppose that ω is differen-tiable on M − ∂M and dω is Le...

The purpose of this article is to explain how pseudo-holomorphic curves in a symplectic 4-manifold can be constructed from solutions to the Seiberg-Witten equations. As such, the main theorem proved here (Theorem 1.3) is an existence theorem for pseudo-holomorphic curves. This article thus provides a proof of roughly half of the main theorem in the announcement [T1]. That theorem, Theorem 4.1, ...

A. Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Outπ1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel’s theorem holds for a compact Lie group G acting ...

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

We will generalize Jaco’s Handle Addition Theorem to the ncompressibility of surfaces on the boundary of 3-manifolds. Several corollaries are given, which show how the theorem can be applied to different situations. 1 The Handle Addition Theorem was first proved by Przytycki [6] in the case when M is a handlebody. In [4] Jaco proved the general version below. Handle Addition Theorem [4] Suppose...

In this article, a two prey - one predator model has been studied where species are competitive in nature and also uses toxic substances for own existence. Biologically well posedness of the system shown through positivity boundedness solutions. Existence criterion stability analysis non-negative equilibrium points have discussed. The sufficient conditions existence Hopf bifurcation switches in...

We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In thin manifold, we complex length short closed geodesic. These results quantify filling theorem Brock Bromberg, extend previous authors from finite volume 3-manifolds to any tame 3-manifold. To prove main results, assemble tools Kleinian group theory i...