bio  website  williewong.wordpress.com 

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age  32  
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A mathematician specializing in nonlinear hyperbolic PDEs, geometric analysis of pseudoRiemannian manifolds, and general relativity.
18h

awarded  mp.mathematicalphysics 
1d

answered  Minkowski spacetime in Newman Penrose formalism 
1d

answered  The Laplacian of an expression involving the Ricci tensor 
1d

comment 
The Laplacian of an expression involving the Ricci tensor
I am slightly confused by your notation: do you mean to first fix some $x$ and consider the function $y\mapsto \triangle_y (Ric_y(\exp_y^{1} x, \exp_y^{1} x))$ (welldefined in some neighbourhood of $x$), and then evaluating it at $y = x$? 
1d

answered  Reference request for the focussing example 
Aug
21 
comment 
Vector Fields in a Riemannian Manifold
@DeaneYang: yes. But then you need the fact that the Laplacian uniquely determines the metric. Which you get by looking at its principal part, and then we come back to Tobias' comments. (In any case, if you are talking about my tendency to provide lowbrow answers on MO, I am definitely guilty as charged. :p) 
Aug
21 
comment 
Inequality for a gradient of a function in Holder space
Just take $X$ any fixed invertible linear transformation. Then we have that $\nabla X$ is a constant matrix, and so is the inverse transformation. You then have that $\\nabla X\_\gamma = \nabla X_0$. Then do scaling as Anthony Quas suggested. 
Aug
21 
answered  Vector Fields in a Riemannian Manifold 
Aug
13 
answered  Conditions on a Lorentzian manifold to ensure existence of global propertime foliation? 
Aug
13 
comment 
Conditions on a Lorentzian manifold to ensure existence of global propertime foliation?
What do you mean by "tangent vector field" $\vec{t}$ of a "time function"? Do you just mean the metric dual vector to the differential? 
Aug
13 
comment 
Conditions on a Lorentzian manifold to ensure existence of global propertime foliation?
... in the diamond. 
Aug
13 
comment 
Conditions on a Lorentzian manifold to ensure existence of global propertime foliation?
Flowing is not enough. After normalizing the flow may not be complete. Furthermore the incompleteness may occur at different "times". For an extremely simple example, look at the diamond $x + t < 1$ in 1+1 Minkowski space which is globally hyperbolic. Pick any GH foliation such that along $\{x = 0\}$ the normal vector lines up with the $t$axis. A propertime foliation built from this GH foliation will have total proper time length of $2$. But for every $\epsilon$ there exists a point $p$ in the diamond such that any timelike curve of length $>\epsilon$ through $p$ cannot be contained... 
Jul
21 
awarded  Popular Question 
Jun
30 
revised 
Does strong convergence in $W_p^1$ imply strong convergence of derivatives of absolute values in $L_p$?
edited title 
Jun
30 
answered  Equivalent Norms on Sobolev Spaces 
Jun
30 
answered  An inequality with critical Sobolev exponent 
Jun
30 
comment 
An inequality with critical Sobolev exponent
For the example Pietro gave, doesn't $\v_\epsilon\_p$ for $p < 2^*$ (where $v_\epsilon = \epsilon^{n/2^*} u(x / \epsilon)$) go to zero for $\epsilon \to 0$? How is adding $\u\_p^{p/2}$ supposed to help? (With the $\epsilon$ in front it can only help if it diverges...) 
Jun
22 
answered  Positive solutions to Yamabe problem? 
Jun
22 
comment 
Positive solutions to Yamabe problem?
I don't understand how your displayed equation has anything to do with the paragraphs above. The conformal change equation for scalar curvature is wellknown (see Wikipedia or this article), and is definitely nonlinear. It differs from your linear equation. Did you mean to have a term $u^q$ for some $q$ on the right hand side? 
Jun
18 
answered  Fourier series and transform related to Epicycles 