Naqing Xie

Critical Points of Wang–Yau Quasi-Local Energy

In this paper, we prove the following theorem regarding the Wang–Yau quasi-local energy of a spacelike two-surface in a spacetime: Let Σ be a boundary component of some compact, time-symmetric, spacelike hypersurface Ω in a time-oriented spacetime N satisfying the dominant energy condition. Suppose the induced metric on Σ has positive Gaussian curvature and all boundary components of Ω have positive mean curvature. Suppose H ≤ H0 where H is the mean curvature of Σ in Ω and H0 is the mean curvature of Σ when isometrically embedded in

Rotating systems, universal features in dragging and antidragging effects, and bounds of angular momentum

{\mathbb R^3}

Some estimates of Wang?Yau quasilocal energy

. If Ω is not isometric to a domain in

Toroidal trapped surfaces and isoperimetric inequalities

{\mathbb R^3}

Brown-york mass and the Thorne hoop conjecture.

, then 1.the Brown–York mass of Σ in Ω is a strict local minimum of the Wang–Yau quasi-local energy of Σ.2.on a small perturbation