Existence and uniqueness to a fully non-linear version of the Loewner-Nirenberg problem

PDE Seminar
Tuesday, February 25, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Yanyan Li – Rutgers University – yyli@math.rutgers.eduhttps://sites.math.rutgers.edu/~yyli/
Xukai Yan

We consider the problem of finding on a given bounded and smooth
Euclidean domain \Omega of dimension n ≥ 3 a complete conformally flat metric whose Schouten
curvature A satisfies some equation of the form  f(\lambda(-A)) =1. This generalizes a problem
considered by Loewner and Nirenberg for the scalar curvature. We prove the existence and uniqueness of
locally Lipschitz solutions. We also show that the Lipschitz regularity is in general optimal.