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Mohammad Javaheri

  1. Semigroups of real functions with dense orbits.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Mohammad Javaheri
    Subjects: Dynamical Systems
    Abstract

    Let ${\mathcal F}_I=\{f:I \to I| f(x)= (Ax+B)/(Cx+D); AD-BC \neq 0 \}$, where
    $I$ is an interval. For $x\in I$, let ${\Omega}_x$ be the orbit of $x$ under
    the action of the semigroup of functions generated by $f,g \in {\mathcal F}_I$.
    Our main result in this paper is to describe all $f,g \in {\mathcal F}_I$ such
    that $\Omega_x$ is dense in $I$ for all $x$.

  2. Convergence of Ricci flow on $\mathbb{R}^2$ to flat space.

    Tue, 08/18/2009 - 11:53 — SomNambul
    Authors: James Isenberg, Mohammad Javaheri
    Subjects: Differential Geometry
    Abstract

    We prove that, starting at an initial metric $g(0)=e^{2u_0}(dx^2+dy^2)$ on
    $\mathbb{R}^2$ with bounded scalar curvature and bounded $u_0$, the Ricci flow
    $\partial_t g(t)=-R_{g(t)}g(t)$ converges to a flat metric on $\mathbb{R}^2$.

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