Séminaire d'Analyse

Solutions to the $\sigma_k$-Loewner-Nirenberg problem are not differentiable

Name: Solutions to the $\sigma_k$-Loewner-Nirenberg problem are not differentiable
Start: 2023-09-04T14:00:00+02:00
End: 2023-09-04T15:00:00+02:00
Location: Amphi Schwartz

par Luc Nguyen (Oxford)

lundi 4 sept. 2023, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

Description

A classical result of Loewner and Nirenberg asserts that on every bounded smooth Euclidean domain there exists a unique smooth complete conformally flat metric of constant negative scalar curvature. I will discuss recent joint works with Maria del Mar Gonzalez, Yanyan Li and Jingang Xiong on existence, uniqueness and regularity for fully nonlinear versions of the Loewner-Nirenberg problem. In particular, I will discuss how minimal surface theory is used to deduce the non-differentiability of solutions when the boundary of the domain is disconnected.