Linked Questions
7 questions linked to/from $C^1$ isometric embedding of flat torus into $\mathbb{R}^3$
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John Nash's Mathematical Legacy
It would seem that John Nash and his wife Alicia died tragically in a car accident on May 23, 2015 (reference). My condolences to his family and friends.
Maybe this is an appropriate time to ask a ...
28
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answers
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Creating high quality figures of surfaces
I am not sure if this question is suitable for mo, it is more about visualization than math. Anyway, here it is:
What is the best way to visualize a 2-surface in Euclidean space with high quality?
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22
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Eversion of the 6-sphere in 7-space
Say that $S^n$ "admits eversion" if the inclusion $S^n \rightarrow \mathbb{R}^{n+1}$ is regularly homotopic to the antipodal map (where a "regular" homotopy is a continuous path through immersions).
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9
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2
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Is there a $W^{2,2}$ isometric embedding of the flat torus into $\mathbb{R}^3$?
It is well known that there exists a $C^1$ isometric embedding of flat torus into $\mathbb{R}^3$, and that this embedding cannot be $C^2$.
Is there a $W^{2,2}$ isometric embedding? (i.e an isometric ...
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1
answer
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embeddings of product of spheres in Euclidean spaces [closed]
I notice that $T^2=S^1\times S^1$ can be embedded in $\mathbb{R}^3$ as a hypersurface (submnaifolds of codimension 1).
In general,
(1). could the product of spheres $S^{m_1}\times\cdots\times S^{...
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1
answer
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Area of square to wrap a torus
The Nash-Kuiper
$C^1$ isometric embedding of flat torus into $\mathbb{R}^3$
has recently been spectacularly visualized by the
Hevea Project.
This suggests two questions.
Q1. What is the area of the ...
9
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1
answer
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Reference for a PL flat torus embedding in $\mathbb{R}^3$
A piecewise linear flat torus embedded in $\mathbb{R}^3$ is shown at http://www.mathcurve.com/polyedres/toreplat/toreplat.shtml.
It is flat in the sense that the angle defect at the vertices is zero.
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