bio | website | williewong.wordpress.com |
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location | ||
age | 31 | |
visits | member for | 5 years, 5 months |
seen | Jun 30 at 12:21 | |
stats | profile views | 9,784 |
A mathematician specializing in nonlinear hyperbolic PDEs, geometric analysis of pseudo-Riemannian manifolds, and general relativity.
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 well-known (see Wikipedia or this article), and is definitely non-linear. 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 |
Jun 18 |
comment |
Kerr metric affine parameter
which means you are asserting that $l$ and $n$ are geodesic vector fields, and the geodesics involved are their integral curves. // Anyway, as I remarked in my second comment, translations of affine parameters (of a given geodesic) are also affine parameters. Is that sufficient to solve your problem? |
Jun 18 |
comment |
Kerr metric affine parameter
Your edit entirely missed the meaning of my comment. |
Jun 18 |
comment |
Kerr metric affine parameter
Regardless, if $\gamma\subset M$ is a geodesic and $r,s:M\to \mathbb{R}$ two functions such that $\mathrm{d}r = \mathrm{d}s$, then if $s|_\gamma$ affinely parametrizes $\gamma$ it is obvious that $r|_\gamma$ is also an affine parametrization. (In any simply connected neighborhood, $ds = dr \implies s = r + c$ for some constant...) |
Jun 18 |
comment |
Kerr metric affine parameter
Affine parameter for what? (Those words are usually used to describe the parametrization of a particular [family of] geodesics. You have not told us what the geodesics are.) |
Jun 16 |
awarded | Notable Question |
Jun 10 |
answered | Separable coordinate systems for the Laplace and Helmholtz equations? |
Jun 9 |
comment |
Should we post on arXiv only papers in publishable shape (or very close)?
On the other hand, now that there is a precedent of publishing the incomplete scribblings of mathematicians, maybe posting very rough drafts on arXiv is just accelerating the inevitable. (If it is not clear, both comments of mine are written with my tongue firmly in my cheek.) |
Jun 9 |
comment |
Should we post on arXiv only papers in publishable shape (or very close)?
Prince would probably say yes (to your title question). I wouldn't really care what you do, but if your intent is to "share the current state of our work" you probably should have a write-up that is "readable". In practical terms I don't see that as being much different from "publishable" (this is, perhaps, more a commentary on how I wish some authors spend more time polishing their papers before actually publishing them, than anything else.) |
Jun 9 |
answered | Differentiability of polytope shadow areas |
Jun 9 |
comment |
Differentiability of polytope shadow areas
For $d = 2$ and $P$ a regular polygon, $\sigma$ can be computed explicitly in principle. Do you have that computation done? |
Jun 9 |
comment |
Energy Oscillations in a One Dimensional Crystal
Given your specific questions it seems that you are asking for an evaluation of the paper that you attached. Your general question seems to be asking about a literature search. Please see our previous Meta discussions on whether such questions are on-topic at MathOverflow: literature search, correctness of papers (though this last discussion focuses more on preprints). |
Jun 9 |
comment |
Energy Oscillations in a One Dimensional Crystal
Points 1-4 seems to be direct quotes from the article. Maybe you should make that clear by (at the very least) putting quotation marks around them. |