On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations
Yamabe's problem in Riemannian geometry -- to find a conformal transformation which sends the scalar curvature \(R\) to a constant \(\widetilde R\) -- is solved here for negative \(\widetilde R\) and 3- dimensional, orientable, compact, smooth manifolds \(M\) with boundary \(\partial M\). Additionally, criteria for conformal compactification are presented and some of the results hold for any dimension \(n\) of \(M\). The improvements concern also the analytical methods: weighted Hölder spaces, asymptotic expansions,... The authors discuss the motivation by the initial value problem to Einstein's equations, too.
scientific article; zbMATH DE number 97875