Scalar Curvature Deformation and a Gluing

Construction for the Einstein Constraint Equations

报告人：刘梦梁

时间：2021-11-16 14:30－16:30pm

地点：数信学院103

摘要：On a compact manifold, the scalar curvature map at generic metrics is a local surjection [F-M]. We show that this result may be localized to compact subdomains in an arbitrary Riemannian manifold. The method is extended to establish the existence of asymptotically flflat, scalar-flflat metrics on Rn (n ≥ 3) which are spherically symmetric, hence Schwarzschild, at infifinity, i.e. outside a compact set. Such metrics provide Cauchy data for the Einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically Schwarzschild near spatial infifinity.