1,735 reputation
627
bio website www-ian.math.uni-magdeburg.de/…
location Magdeburg, Germany
age 31
visits member for 3 years, 7 months
seen Jul 16 at 0:38

I am an Australian mathematician.


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.
Sep
1
comment existence of a map between $\mathbb R^2$ and $\mathbb R$
And if we drop the continuity hypothesis?
Jun
11
comment 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?
Jun
8
awarded  Caucus
Jun
4
comment 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.
May
31
comment 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.