Past Seminars- Analysis

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  • Changfeng Gui
    Tue Mar 14, 2017
    3:00 pm
    In this talk, I will introduce a new geometric inequality:  the Sphere Covering Inequality. The inequality  states that   the  total area  of two {\it distinct}  surfaces with Gaussian curvature  less than 1,   which  are also conformal to  the Euclidean unit disk  with the same...
  • Xiaodong Wang
    Tue Mar 7, 2017
    4:00 pm
    Given a compact Riemannian manifold with nonnegative Ricci curvature and convex boundary it is interesting to estimate its size in terms of the volume, the area of its boundary etc. I will discuss some open problems and present some partial results.   This is a joint seminar with geometry.
  • Russell Brown
    Tue Mar 7, 2017
    3:00 pm
    We consider the scattering map introduced by Beals and Coifman and Fokas and Ablowitz that may be used to transform one of the Davey Stewartson equations to a linear evolution. We give mapping properties of the scattering transform on weighted L^2  Sobolev spaces that mimic well-known properties of the Fourier transform....
  • Jeffrey Case
    Tue Feb 7, 2017
    3:00 pm
    The P-prime operator is a CR invariant operator on CR pluriharmonic functions and is closely related to a sharp Moser--Trudinger-type inequality in CR manifolds.  I will describe some analytic and geometric properties of this operator, and in particular use it to solve a nonlinear PDE of critical order which is the CR analogue of the Q-...
  • Hanlong Fang
    Tue Nov 1, 2016
    3:03 pm
    We discuss a new rigidity property for local volume preserving maps between hermitian symmetic spaces of compact type along the lines of recent work of Clozel-Ullmo and Mok-Ng.  This is a joint work with Prof. X.Huang and Dr. X.Ming.
  • Jinxin Xue
    Tue Oct 25, 2016
    3:00 pm
     Lyapunov exponents measure the rate of exponential expansion or contraction in a dynamical system. For a given nonlinear dynamical systems, it turns out to be a very hard problem to prove the nonvanishing of Lyapunov exponents or even to estimate them quantitatively. For a given prototypical two-dimensional map, we introduce a small random...
  • Bingyuan Liu
    Tue Oct 18, 2016
    3:00 pm
    Geometric analysis in differential geometry is a powerful tool in Riemannian geometry. It has been used to solve many problems in Riemannian geometry. In the field of several complex variables, it was not the most popular weapon to attack questions. One of the reasons is that many problems in the several complex variables relates to some types of...