Piotr Chrusciel , Puskar Mondal , Bowen Zhao

Xuantao Chen

Tuesday, October 13, 2026 4:30 PM - 5:30 PM

Tsinghua-Jingzhai-105

Zoom 712 322 9571 (BIMSA)

We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that once appropriate gauge conditions have been chosen and four scalars freely specified (modulo $\ell\leq 1$ modes), we can rewrite the constraint equations as a well-posed system of coupled transport and elliptic equations on two-spheres. Our method can be applied to construct various types of initial data, including data with arbitrarily fast decay, borderline decay, and short-pulse type data. This is joint work with Sergiu Klainerman.