Nonlinear stability of the slowly-rotating Kerr-de Sitter family

In this paper, we provide a new proof of nonlinear stability of the slowly-rotating Kerr-de Sitter family of black holes as a family of solutions to the Einstein vacuum equations with cosmological constant $\mathrm{\Lambda }>0$, originally established by Hintz and Vasy in their seminal work [arXiv:1606.04014]. Using the linear theory developed in an upcoming companion paper, we prove the nonlinear stability of slowly-rotating Kerr-de Sitter using a bootstrap argument, avoiding the need for a Nash-Moser argument, and requiring initial data small only in the $H^6$ norm.