Geometric inequalities and the hoop conjecture
- 1 September 1992
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 9 (9) , L105-L110
- https://doi.org/10.1088/0264-9381/9/9/001
Abstract
Geometric inequalities holding for any convex body and connecting the perimeter of plane curves associated with this body to the total mean curvature of its boundary are proved. Their application to some analytic models of nonspherical collapse yields a more precise formulation of the hoop conjecture.Keywords
This publication has 16 references indexed in Scilit:
- Nonexistence of apparent horizons for elongated configurations of matter having small massClassical and Quantum Gravity, 1992
- Trapped surfaces in expanding open universesPhysical Review D, 1992
- Analytic models of nonspherical collapse, cosmic censorship and the hoop conjecturePhysics Letters A, 1991
- Hoop conjecture for black-hole horizon formationPhysical Review D, 1991
- Hoop conjecture and trapped surfaces in nonspherical massive systemsPhysical Review Letters, 1991
- Trapped surfaces due to concentration of matter in spherically symmetric geometriesClassical and Quantum Gravity, 1989
- Must nonspherical collapse produce black holes? A gravitational confinement theoremPhysical Review Letters, 1986
- The formation of black holes in nonspherical collapse and cosmic censorshipCanadian Journal of Physics, 1986
- The existence of a black hole due to condensation of matterCommunications in Mathematical Physics, 1983
- Slowly Rotating Relativistic Stars.VI. Stability of the Quasiradial ModesThe Astrophysical Journal, 1972