8,549 reputation
12774
bio website people.epfl.ch/willie.wong
location Lausanne, Switzerland
age 31
visits member for 4 years, 8 months
seen 10 hours ago
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 Levi-Civita 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 hyperboloid-line 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 n-dimension 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 Gauss-Bonnet and integrating scalar curvature (so the formula you gave is arguably not the correct definition for higher genus surfaces). The higher dimensional Gauss-Bonnet 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 Hausdorff-ness 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 well-known local existence theorem of Choquet-Bruhat, 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 (general-relativity) 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 pseudo-Riemannian 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.