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| bio | website | www-ian.math.uni-magdeburg.de/… |
|---|---|---|
| location | Magdeburg, Germany | |
| age | 30 | |
| visits | member for | 2 years, 5 months |
| seen | 12 hours ago | |
| stats | profile views | 479 |
I am an Australian mathematician.
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Apr 12 |
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Periodic polynomial? This is wrong -- consider $\prod (1/n)$. |
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Nov 15 |
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characterizing semi-Riemannian spaces of constant curvature Hi Jason. Your example of $S^2\times S^2$ is not with the metric I normally consider (I normally take the flat metric on $S^2\times S^2$). With the round metric, is this still a smooth manifold? Does the condition $\nabla R = 0$ make sense at the transition lines from positive to zero curvature? It seems to me that there are regions with constant positive curvature, and constant zero curvature, and nothing in-between.... I'm probably being dense, but could you shed some light on this? |
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Oct 14 |
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An inequality in Evans' PDE It is just $ab \le \frac12a^2 + \frac12b^2$. |
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Oct 14 |
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inverting a cone to a torus You should just edit the one answer... |
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Oct 13 |
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An inequality in Evans' PDE This is just Peter-Paul: the C is not really the same C as on the left. It is $ C^2/2$. |
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Oct 10 |
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A positive “Fourier transform” is integrable What does the complex plane in the subscript mean? |
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Oct 8 |
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signed curvature If this is homework, please add the homework tag. |
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Oct 6 |
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Total mean curvature in $L^2$ and minimal surfaces in spaces with non-positive sectional curvature Oh! I had a notational mix-up. That's one problem I don't see ever being solved in differential geometry: some semblance of unification of notation. Nice answer. |
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Oct 5 |
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Total mean curvature in $L^2$ and minimal surfaces in spaces with non-positive sectional curvature I don't understand the application of G-B here. I'm probably being dense, but I thought we had $\int K = 4\pi$ and not $\int S = 8\pi$. (The $S$ is the scalar curvature of the background space, and should be negative, right?) Perhaps you could add a bit more detail there for the slowpokes like me. |
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Oct 5 |
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Total mean curvature in $L^2$ and minimal surfaces in spaces with non-positive sectional curvature Thanks for the answer. I think you'll find that the mean curvature scales like $r^{-1}$; this is easy to remember from the scale invariance of the Willmore energy in Euclidean space: the measure scales like $r^2$ and so the integrand $H^2$ must scale like $r^{-2}$. Or just from thinking about the prinicipal curvatures, which must scale like $r^{-1}$. |
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Sep 28 |
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How do I interpret $F_1, \neg F_1 \vdash F_2$ @Jiew If you know both $F_1$ and $not F_1$ then you have a contradiction. A falsehood. An example is that both the propositions $1+1 = 2$ and $1+1 = 3$ are valid for whatever reason. The rule in your question then gives ANYTHING as a valid consequence. For example, you could conclude $1+1 = 73$, $pigs fly$ or whatever you like. |
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Sep 18 |
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Constant tensors and covariant derivatives @Yuri Yes, you're right, it doesn't vanish and will involve second fundamental forms. Also, I think the answer to my other question is no. I guess this question can be closed or if it is preferable I can answer it myself. |
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Sep 18 |
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Constant tensors and covariant derivatives @Yuri I mean for $\text{Ric}$ to act on $T\Sigma$, although I'm not sure if it turns out to be better for it to act on the pullback bundle. Can you explain why you don't think the expression is well-defined either way? Let's just take $X\in\{e_1,e_2\}$. What I mean by "connection in the normal bundle" is just the projection of $\nabla$ onto $(T\Sigma)^\perp$. Sorry that I am being confusing. |
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Sep 18 |
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Constant tensors and covariant derivatives @Yuri (1) By restricting $\text{Ric}$ to $\Sigma$. (This involves composition with the immersion map.) (2) $D$ induces a connection in the normal bundle, and this acts "in the normal direction". |
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Sep 3 |
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existence of a map between $\mathbb R^2$ and $\mathbb R$ I guess I was too subtle in my suggestion that the addition of a note to the effect of "The existence of a bijection is clear, it is the additional continuity hypothesis that is at work here." could improve the answer. |
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Sep 1 |
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existence of a map between $\mathbb R^2$ and $\mathbb R$ And if we drop the continuity hypothesis? |
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Jun 11 |
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Generalization of ellipse equation to higher dimensional surfaces I would guess this is highly dependent on the magnitude of $c$ in relation to the width of the one-dimensional ellipse $e$. In particular, if $c$ is too small, $S$ is empty. Is this really what you want? |
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Jun 4 |
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differential and arc length notation question @soup This is totally standard when we take as a measure something induced by the map we are studying. You can see this same computation coming up in the first variation of the area element. I'm not sure what you mean by transport theorem. |
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May 31 |
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Usage of the word “formal(ly)” This is just an English language quirk. There are two basic meanings of 'formal' -- something related to 'form', which is not what you have in mind (despite being what Jazwinksi has in mind), and being rigorous. Mathematicians typically use the word rigorous when they mean rigorous. |
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Mar 23 |
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Does every closed curve contain the vertices of a square? The question is essentially settled for $C^2$ curves, locally graphical curves if we restrict ourselves to one codimension. There is still more to be done (rectifiable curves would be interesting). |
