1,775 reputation
729
bio website www-ian.math.uni-magdeburg.de/…
location Magdeburg, Germany
age 31
visits member for 3 years, 10 months
seen Oct 10 at 19:56

I am an Australian mathematician.


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awarded  Explainer
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awarded  Necromancer
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awarded  Nice Answer
Jul
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comment Soft question: How does basic differential geometry “fit together”?
You're not looking for a book recommendation, you just want a high-level map? The problem is that there is no way to fit even just the names and connections between all topics in diff geom on one page. You're going to have to be more specific.
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awarded  Curious
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awarded  Notable Question
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awarded  Good Answer
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awarded  Yearling
Oct
30
revised How solve this equation
Tag incorrect
Oct
30
suggested suggested edit on How solve this equation
Sep
27
awarded  Popular Question
Sep
10
comment How to solve this quasilinear parabolic evolution equation (result of curve shortening flow)?
It is just a one dimensional quasilinear parabolic PDE... this is covered by standard theory. Can you explain more which texts you looked at? Did you check Lieberman for example?
Sep
6
comment Geometric Interpretation: Parallel forms are harmonic
See the answer for the first question. For the second: It isn't an arbitrary solution of the Laplacian, it's the Laplacian acting on the volume form.
Sep
2
comment Geometric Interpretation: Parallel forms are harmonic
The fact that the volume form is parallel implies that infinitesimal deformations of the volume form act exactly linearly. Since the Levi-Civita connection controls also the cotangent deformations, this implies that the volume form expands linearly in every possible direction. This is stronger than $\Delta \mu = 0$!
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awarded  Revival
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comment Periodic polynomial?
This is wrong -- consider $\prod (1/n)$.
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awarded  Nice Question
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awarded  Yearling
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