BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Isoperimetric mass and isoperimetric surfaces in AF manifolds Shi, Yuguang


The notion of isoperimetric mass was introduced by Prof. Huisken about ten years ago, and it has deep relation with ADM mass of an asymptotically flat manifold. In the first part of talk I will discuss non negativity of isoperimetric masses of isoperimetric regions in a 3-dim asymptotically flat manifold with nonnegative scalar curvature. More precisely, I will show that for any isoperimetric region , its isoperimetric mass is always non less than a nonnegative quantity which is in terms of Hawking mass, and it is equal to zero if and only if the AF manifold is isometric to the 3-dim Euclidean space. In the second part of this talk, I will mention an application of isoperimetric mass, i.e. by estimate of isoperimetric masses, I will show that any sequence of isoperimetric regions with enclosed volumes tending to infinity cannot drift off to the infinity on any 3-dim asymptotically flat manifold with nonnegative scalar curvature. If time allowable, I will mention some similar results in the setting of asymptotically hyperbolic case.

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