Hamiltonian F-Stability of Complete Lagrangian Self-Shrinkers

Smooth Compactness of Self-shrinkers

We prove a smooth compactness theorem for the space of embedded selfshrinkers in R. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow. 0. Introduction A surface Σ ⊂ R is said to be a self-shrinker if it satisfies (0.1) H ...

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

Supplement on Lagrangian, Hamiltonian Mechanics

⋆ When there are several independent variables it is easy to make mistakes in taking partial derivatives. The fundamental rule is: always know which set of independent variables is in use, so that you are sure which are being held fixed during the process of taking a partial derivative. ⋆ A simple example will illustrate the problems that await the careless. Start with f(x, y) = 2x + y; ∂f/∂x =...

Stability of F-biharmonic maps

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

Complete Lagrangian of Mssm*

A brief derivation of the lagrangian of the minimal supersymmetric theory is given and the complete expression of the lagrangian in terms of mass eigenstates is presented.