Generalized Obata theorem and its applications on foliations

Lichnerowicz and Obata Theorems for Foliations

The standard Lichnerowicz comparison theorem states that if the Ricci curvature of a closed, Riemannian n-manifold M satisfies Ric (X,X) ≥ a (n − 1) |X| for every X ∈ TM for some fixed a > 0, then the smallest positive eigenvalue λ of the Laplacian satisfies λ ≥ an. The Obata theorem states that equality occurs if and only if M is isometric to the standard n-sphere of constant sectional curvatu...

A Generalized Mazur’s Theorem and Its Applications

We generalize a theorem of Mazur concerning the universal norms of an abelian variety over a Zp-extension of a complete local field. Then we apply it to the proof of a control theorem for abelian varieties over global function fields.

Fan-KKM Theorem in Minimal Vector Spaces and its Applications

In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.

Generalized Bezout's theorem and its applications in coding theory

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more plane curves. A new approach to determine a lower bound on the minimum distance for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient l...

Generalized Product Theorem for the Mellin Transform and Its Applications