We investigate the stability of the Positive Mass Theorem for three‐dimensional axisymmetric manifolds. It is widely known that asymptotically at manifolds with nonnegative scalar curvature have nonnegative ADM mass, and that the only asymptotically at manifold with nonnegative scalar curvature and zero ADM mass is Euclidean space.
We will show that axisymmetric manifolds with nonnegative scalar curvature and small ADM mass, and which satisfy an additional technical assumption, are close to Euclidean space in a Sobolev sense.
Edward Bryden (Tübingen): Stability of the positive mass theorem for axisymmetric manifolds
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