1,785 reputation
929
bio website www-ian.math.uni-magdeburg.de/…
location Magdeburg, Germany
age 31
visits member for 4 years
seen Dec 3 at 0:15

I am an Australian mathematician.


Nov
15
comment 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?
Oct
14
answered An inequality in Evans' PDE
Oct
14
comment An inequality in Evans' PDE
It is just $ab \le \frac12a^2 + \frac12b^2$.
Oct
14
comment inverting a cone to a torus
You should just edit the one answer...
Oct
13
comment 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$.
Oct
10
comment A positive “Fourier transform” is integrable
What does the complex plane in the subscript mean?
Oct
8
comment signed curvature
If this is homework, please add the homework tag.
Oct
7
asked Is there a proof of Benford's Law?
Oct
6
answered Reversing the Ricci flow
Oct
6
comment 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.
Oct
5
comment 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.
Oct
5
comment 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 $r^{-1}$.
Sep
28
comment 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.
Sep
28
answered How do I interpret $F_1, \neg F_1 \vdash F_2$
Sep
28
asked Total mean curvature in $L^2$ and minimal surfaces in spaces with non-positive sectional curvature
Sep
18
comment 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.
Sep
18
comment 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.
Sep
18
comment 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".
Sep
18
asked Constant tensors and covariant derivatives
Sep
3
comment 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.