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Results tagged with dg.differential-geometry
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user 2480
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
7
votes
Accepted
Can the thief escape (from a smooth, simple closed curve)?
Claim. The thief $T$ can escape if $C$ is a circle, with a simple strategy of dribbling left and right each policeman at a time in such a way that he is left out of reach of the thief no matter what t …
- 5,103
4
votes
Is it possible to capture a sphere in a knot?
Adding to Zeb's proof that the tetrahedron can be deformed, one should notice that any tassellation of the sphere containing at least one hexagon (fullerene type) won't be rigid either. In fact alrea …
- 5,103
3
votes
Is it possible to capture a sphere in a knot?
Since Anton's beautiful solution makes use of the symmetry of the sphere, I wonder how similar
results could be proven, or counterexamples given, for any other convex shape, including
2-dimensional on …
- 5,103
2
votes
Is it possible to capture a sphere in a knot?
It seems that both the 2-agon and the octahedron (which after all is a collection of 3 somewhat constrained 2-agons) can be shrunk off the sphere, but with 0 derivative at the start, which means that …
- 5,103
2
votes
Is it possible to capture a sphere in a knot?
Reid, excellent proof. It works for the cube too and even kills the icosahedron. In this last case I don't know what the angles of a triangle are exactly, so let's just say 60+ each.
Then joining ea …
- 5,103
0
votes
Can the thief escape (from a smooth, simple closed curve)?
The cops should always win. Here is a sketch of a proof.
One cop (for short) trying to catch the thief crossing a segment: the cop can run on the segment at top speed towards the thief (provided the …
- 5,103