On the Bartnik mass of apparent horizons

G. D. Birkhoff, Dynamical systems with two degrees of freedom , Trans. Amer. Math. Soc. 18

1917

Earlier work this paper cites.

P. M. Pu, Some inequalities in certain nonorientable Riemannian manifolds , Pacific J. Math. 2

1952

Earlier work this paper cites.

S. W. Hawking, Black holes in general relativity , Comm. Math. Phys. 25

1972

Earlier work this paper cites.

K. S. Thorne, Nonspherical gravitational collapse: A short review , p. 231, 1972

1972

Earlier work this paper cites.

R. S. Hamilton, The inverse function theorem of Nash and Moser , Bull. Amer. Math. Soc. (N.S.) 7

1982

Earlier work this paper cites.

C. B. Croke, Area and the length of the shortest closed geodesic , J. Differential Geom. 27

1988

Cited alongside, same era.

R. Bartnik, New definition of quasilocal mass , Phys. Rev. Lett. 62

1989

Cited alongside, same era.

E. Calabi and J. Cao, Simple closed geodesics on convex surfaces , J. Differential Geom. 36

1992

Cited alongside, same era.

A. D. Rendall, The initial value problem for a class of general relativistic fluid bodies , J. Math. Phys. 33

1992

Cited alongside, same era.

by same author, Quasi-spherical metrics and prescribed scalar curvature , J. Differential Geom. 37

1993

Cited alongside, same era.

G.W. Gibbons, Birkhoff’s invariant and Thorne’s hoop conjecture , preprint (arXiv: 0903.1580)

Cited in the paper.

C. Y. Lin and C. Sormani, Bartnik’s mass and Hamilton’s modified ricci flow

Cited in the paper.

J. Corvino, Scalar curvature deformation and a gluing construction for the Einstein constraint equations , Comm. Math. Phys. 214

2000

Later among the works it cites.

H. Bray, Proof of the Riemannian Penrose inequality using the positie mass theorem , J. Differential Geom. 59

2001

Later among the works it cites.

G. Huisken and T. Ilmanen, The inverse mean curvature flow and the Riemannian Penrose inequality , J. Differential Geom. 59

2001

Later among the works it cites.

M. Cvetič, G. W. Gibbons, and C. N. Pope, More about Birkhoff’s invariant and Thorne’s hoop conjecture for horizons , Classical Quantum Gravity 28

2011

Later among the works it cites.

B. Smith, Black hole initial data with a horizon of prescribed intrinsic and extrinsic geometry , Complex analysis and dynamical systems IV. Part 2, Contemp. Math., vol. 554, Amer. Math. Soc., Providence, RI, 2011, pp. 229–244. MR 2884405