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5 papers · 2 filters
Rigidity and minimizing properties of quasi-local mass
Po-Ning Chen, Mu-Tao Wang
In this article, we survey recent developments in defining the quasi-local mass in general relativity. We discuss various approaches and the properties and applications of the diff…
Conserved Quantities of harmonic asymptotic initial data sets
Po-Ning Chen, Mu-Tao Wang
In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these defini…
Conserved quantities on asymptotically hyperbolic initial data sets
Po-Ning Chen, Mu-Tao Wang, Shing-Tung Yau
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give…
The Ricci flow on the sphere with marked points
D. H. Phong, Jian Song, Jacob Sturm +1
The Ricci flow on the 2-sphere with marked points is shown to converge in all three stable, semi-stable, and unstable cases. In the stable case, the flow was known to converge with…
Inverse mean curvature flows in the hyperbolic 3-space revisited
Pei-Ken Hung, Mu-Tao Wang
This note revisits the inverse mean curvature flow in the 3-dimensional hyperbolic space. In particular, we show that the limiting shape is not necessarily round after scaling, thu…