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age 31
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seen Jun 30 at 12:21

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.