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34 videos

4 videos

4 videos

## 2022 - Francophone Computer Algebra Days - Journées nationales de calcul formel

00:00:00 / 00:00:00

## Recent inequalities on the mass-to-capacity ratio

Appears in collection : Not Only Scalar Curvature Seminar

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.

• Date of recording 10/28/22
• Date of publication 11/3/22
• Institution IHES
• Language English
• Audience Researchers
• Format MP4

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