## Analysis and PDE

•  Leonardo Abbrescia, MSU
•  Stability of traveling planewave solutions to Lorentzian vanishing mean curvature flow
•  11/21/2019
•  1:00 PM - 1:50 PM
•  C517 Wells Hall

Lorentzian minimal submanifolds of Minkowski space are the dynamic analogue of minimal surfaces in the elliptic regime. They are defined by the vanishing of mean curvature, which can be expressed as a system of geometric PDEs. With the requirement that the submanifold be Lorentzian, that is, that the induced metric is Lorentzian, the equations have a hyperbolic nature. Consequently, the natural approach to study them is via the Cauchy initial value problem. In this talk we discuss stability properties of traveling planewave solutions to these equations, and highlight the difficulties introduced by the "infinite energy" planewave background. This is joint work with Willie Wong.

## Contact

Department of Mathematics
Michigan State University