Extensions and fill-ins with non-negative scalar curvature

  title={Extensions and fill-ins with non-negative scalar curvature},
  author={Jeffrey L. Jauregui and Pengzi Miao and Luen-fai Tam},
Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown–York mass, to study a fill-in problem of realizing geometric data on a 2-sphere as the boundary of a compact 3-manifold of non-negative scalar curvature. We characterize the relationship between two borderline cases: one in which the Shi–Tam extension has zero total mass, and another in which fill-ins of non-negative… CONTINUE READING
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