The singular Yamabe problem and a fully nonlinear generalization & Vortex desingularization for the 2D Euler equations

(16:00 hrs.)

Title: The singular Yamabe problem and a fully nonlinear generalization 

Abstract: I will begin with an overview of the work of Loewner-Nirenberg on constructing complete conformal metrics of constant negative scalar curvature on domains in Euclidean space, and its extension to Riemannian manifolds with boundary.  I will then describe some fully nonlinear generalizations.  Finally, I will discuss a certain geometric invariant of solutions, called the renormalized volume, and some recent work with Robin Graham on computing closed formulas for these invariants in dimension four.

(17:00 hrs.)

Title: Vortex desingularization for the 2D Euler equations

Abstract: We present a construction of solutions for the 2D Euler equation with highly concentrated vorticity around a finite number of points, which gives a precise asymptotic expansion of the vorticity and velocity. We do this by exploiting a connection with the Liouville equation. This is joint work with J. Dávila , M. Musso  and J. Wei

Posted on Jul 13, 2018 in CAPDE, Seminars