bio  website  people.epfl.ch/willie.wong 

location  Lausanne, Switzerland  
age  31  
visits  member for  4 years, 8 months 
seen  10 hours ago  
stats  profile views  8,663 
PostDoc at the PDE group at EPFL. I tend to like working with evolution equations from general relativity and Lagrangian field theories.
11h

reviewed  Close Isotropic correlation function for a vector valued random field 
1d

reviewed  Close Probability of the maximum of a throw of an infinite number of $n$sided dice being $k$ 
Oct 15 
comment 
“Oldest” bug in computer algebra system?
From looking at the linked arxiv paper it seems that the problem is in that the LeviCivita symbol is defined relative to the Kronecker delta, so that changing one changes the other? (I tried to understand your first two paragraphs and am not sure if I got it right.) If that's the case this is less of a bug in the software but a PEBCAK. 
Oct 15 
reviewed  Leave Open “Oldest” bug in computer algebra system? 
Oct 14 
reviewed  Close Axiomatic Ergodic Theory (book) 
Oct 14 
reviewed  Close Variance along the regression line 
Oct 14 
comment 
ODE system has zero as the only solution?
The general idea to proofs of that type you want is the construction of a monotonicity law. In the question you linked to in your post, the answer Igor gave was to show that your system is dissipative, in that the presence of the $a$ term forces the energy to be monotonically decreasing. While energy may not work for your system, you should still try to find a quantity that is monotonic, which will contradict the periodicity of the solutions. 
Oct 13 
reviewed  Close Direct computation of hyperboloidline intersection in 3d 
Oct 13 
reviewed  Close How many vectors exist satisfying the angle between any two vectors equals to a constant beta(0<beta<pi) in a ndimension Euclid space? 
Oct 13 
comment 
Generalized Hawking Mass
... that term will probably need either a serious replacement or some physical justification why it is the genus that matters and not anything else. 
Oct 13 
comment 
Generalized Hawking Mass
For the usual formula, one thing you need to contend with is the $16\pi$ term inside the parentheses: more generally that term is/should be proportional to the Euler characteristic of your two surface $\Sigma$, and arises actually from GaussBonnet and integrating scalar curvature (so the formula you gave is arguably not the correct definition for higher genus surfaces). The higher dimensional GaussBonnet is more complicated, so ... 
Oct 13 
comment 
Generalized Hawking Mass
One possibility is that you can start with the characterisation of the Hawking mass in spherical symmetry as the "flux relative to the Kodama vector field" and see if it leads you to anything. For the standard 3+1 case you can see the computations on my blog (scroll down a little to the section titled "Kodama vector field"). But whatever it is it should probably agree with the mass of higher dimensional Schwarzschild. 
Oct 10 
comment 
Generalized Hawking Mass
Have you tried asking Carla? (If you are in Tuebingen her office should be somewhere near.) 
Oct 10 
comment 
Topological restrictions from mean curvature bounds
My point is mainly this: I think the question you ask is an interesting one in geometric topology (I even upvoted!). But the question you ask has pretty much absolutely nothing to do with general relativity: certainly you don't expect all initial data sets in GR embed in Euclidean $\mathbb{R}^{1+n}$ as an $n$ hypersurface with constant mean curvature, so your motivation is tenuous at best and entirely nonsensical at worst. So I think removing that tag and the parenthetical can only improve your question. 
Oct 10 
comment 
Topological restrictions from mean curvature bounds
For compact manifolds, under CMC, the situation is entirely characterised (going back to the 80s); in the low regularity setting you can see this paper. In short, the fact that it is CMC does not constraint the topology: the topology does constrain, a little bit, which values the mean curvature can take (positive, negative, or zero). But since you only demand CMC and not the value of mean curvature, there is absolutely no restriction. 
Oct 8 
answered  ODE system has zero as the only solution? 
Oct 8 
comment 
The Cauchy Problem in General Relativity: Existence of a Hausdorff Development
Hausdorff is actually the hardest part of the proof, in some sense. You may be interested in Jan Sbierski's preprint where in section 3.2 he proves the Hausdorffness using a line of argument not too far removed from the one you are thinking about. I am inclined to agree that the original papers may be incomplete when it comes to this point. // edit Ah: I see I have already recommended this paper to you before. Sorry for the noise. 
Oct 8 
comment 
Topological restrictions from mean curvature bounds
More precisely, by the wellknown local existence theorem of ChoquetBruhat, in the context of Einstein's equation there is absolutely no topological restrictions (beyond the initial thing being a smooth manifold) in the "general relativity" question. We can always change the topology of the solution to accommodate. 
Oct 8 
comment 
Topological restrictions from mean curvature bounds
Two side remarks which I am sure you are aware of: in the Einstein constraint equations the ambient manifold is Lorentzian and the topology of the ambient manifold is not necessarily $\mathbb{R}^{n+1}$. (This is not to say that there's something wrong with the question, but your motivation and your tag (generalrelativity) are rather far from the question you actually asked.) 
Oct 8 
comment 
Variation of curvature with respect to immersion?
For the mean curvature alone, in a much more general setting (arbitrary codimension embeddings of pseudoRiemannian manifolds), I computed the first variation of the mean curvature vector in section A.5 of this paper following a variation of what Deane described (using Christoffel symbols instead of frames) here. 