Hardy–Sobolev inequality with higher dimensional singularity

Naked singularity formation for higher dimensional inhomogeneous dust collapse

The Cosmic Censorship Conjecture (CCC)[1,2] states that the space-time singularity produced by gravitational collapse must be covered by the horizon. The CCC is yet one of the unresolved problem in General Relativity. In fact the conjecture has not yet any precise mathematical proof. However the singularity theorems as such do not state anything about the visibility of the singularity to an out...

Theorising inequality : two-dimensional participatory justice and higher education research

This chapter discusses how Nancy Fraser’s theory of two-dimensional participatory justice may be employed in research concerned with inequalities within higher education. The main concepts of Fraser’s theory are discussed and evaluated in the light of the critical attention they have attracted. Following that, I demonstrate the empirical application of Fraser’s ideas through discussion of extra...

Boosted Three-Dimensional Black-Hole Evolutions with Singularity Excision

G. B. Cook,1 M. F. Huq,2 S. A. Klasky,3 M. A. Scheel,1 A. M. Abrahams,4,5 A. Anderson,6 P. Anninos,4 T. W. Baumgarte,4 N. T. Bishop,7 S. R. Brandt,4 J. C. Browne,2 K. Camarda,8 M. W. Choptuik,2 R. R. Correll,2,9 C. R. Evans,6 L. S. Finn,10 G. C. Fox,3 R. Gómez,11 T. Haupt,3 L. E. Kidder,10 P. Laguna,8 W. Landry,1 L. Lehner,11 J. Lenaghan,6 R. L. Marsa,2 J. Masso,4 R. A. Matzner,2 S. Mitra,2 P. ...

Singularity formation in three-dimensional vortex sheets

We study singularity formation of three-dimensional ~3-D! vortex sheets without surface tension using a new approach. First, we derive a leading order approximation to the boundary integral equation governing the 3-D vortex sheet. This leading order equation captures the most singular contributions of the integral equation. By introducing an appropriate change of variables, we show that the lea...

Higher Dimensional