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Results tagged with isoperimetric-problems
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user 13093
7
votes
3
answers
706
views
When is perimeter continuous under Hausdorff convergence?
It is known that the perimeter is lower semicontinuous for the convergence of sets. Two variants are widely known:
(Golab's theorem) in $\Bbb{R}^2$ if the sets $\Omega_n$ converge to $\Omega$ in the …
- 2,222
7
votes
A long-lasting conjecture of Pólya & Szegő
Together with D. Bucur we propose a strategy which could prove the conjecture for a fixed $n \geq 5$ using a finite number of certified numerical computations.
Our paper can be found here: On the poly …
- 2,222
1
vote
Visual proof of convergence for Steiner's symmetrization
Consider $\omega$ a convex shape and $B$ a ball having the same volume centered at a point in $\omega$ (for example the centroid). Define a coordinate system in $\Bbb{R}^d$ and make a Steiner symmetri …
- 2,222
0
votes
When is perimeter continuous under Hausdorff convergence?
I found a paper which deals with the case I'm interested. It shows that for the particular case of minimal relative perimeter sets with given volume constraint the relative perimeter of the minimizers …
- 2,222