Conformal compactification of type (p,q) pseudo-Euclidean spaces
We explain how to conformally compactify pseudo-Euclidean spaces with $(p,q)$ signature.
Blow-up of QNLW with Small Initial Data à la Christodoulou
Lecture slides that Gustav Holzegel and I used for the January 13-14, 2014 OXPDE Workshop at Oxford University.
Approximating Continuous Functions
Expository note on the Runge phenomenon
Purely kinetic initial data for Schwarzschild
Can initial data for Einstein's equation be specified in such a way that all the 'energy' are kinetic and not potential?
Notes on Sobolev Spaces
Lecture notes introducing Sobolev spaces.
Whitney Extension and Counterexample to Sard's Theorem
In a first course in differential geometry/topology we are often taught the following version of Sard's theorem: Theorem …
Non-existence of multiple-black-hole solutions that look locally like subextremal Kerr-Newman
Paper announcement.
The non-existence of black holes in (2+1) dimensional general relativity
We show that trapped surfaces cannot exist in (2+1) dimensional relativity.
Mariş's Theorem
We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.
One and two (space-time) dimensional general relativity
Life is boring in low dimensions.