Description
During the talk, I will present the results obtained in collaboration with Romain Gicquaud concerning the classical construction of initial data using the conformal method, which was originally proposed by Holst, Nagy and Tsogtgerel and later refined by Maxwell. This method transforms the usual constraint equation for initial data in general relativity into a set of two coupled nonlinear elliptic PDEs. Our work revisits the standard proof by removing certain assumptions. In particular, I will explain how our proof guarantees the uniqueness of solutions to the equations of the conformal method as soon as a bound is imposed on the physical volume and how it provides an explicit construction of solutions.