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Recent inequalities on the mass-to-capacity ratio

By Pengzi Miao

On an asymptotically flat 3-manifold, both the mass and the capacity have unit of length, and hence their ratio is a dimensionless quantity. In this talk, I will discuss recent work on establishing new inequalities for the mass-to-capacity ratio on manifolds with nonnegative scalar curvature. Besides revealing additional proofs of the positive mass theorem, applications of these inequalities include new sufficient conditions guaranteeing positive mass via $C^0$-geometry of regions separating the boundary and the infinity. If time permits, a proposal to study manifolds with the mass-to-capacity ratio bounded by one will also be discussed.

Information about the video

  • Date of recording 28/10/2022
  • Date of publication 03/11/2022
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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