Questions tagged [rigidity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
12
votes
2answers
675 views

Are all maps $\mathbb{R}^2 \to \mathbb{R}^2$ with fixed singular values affine?

Let $f:\mathbb{R}^2 \to \mathbb{R}^2$ be a smooth map whose differential has fixed distinct singular values $0<\sigma_1<\sigma_2$ and an everywhere positive determinant (which is the product $\...
9
votes
0answers
161 views

How to correctly state Cauchy's rigidity theorem?

Cauchy's rigidity theorem is usually cites briefly as Any two (convex, 3-dimensional) polyhedra with pairwise congruent faces are themselves congruent. As a more formal generalization to general ...
24
votes
3answers
1k views

Which mapping class group representations come from algebraic geometry?

Let $\Gamma_g$ be the mapping class group of a closed oriented surface $\Sigma$ of genus $g$. There is a natural surjection $t \colon \Gamma_g \to \mathrm{Sp}(2g,\mathbf Z)$ which sends a mapping ...
5
votes
3answers
527 views

Alexandrov's generalization of Cauchy's rigidity theorem

Wikipedia states that A. D. Alexandrov generalized Cauchy's rigidity theorem for polyhedra to higher dimensions. The relevant statement in the article is not linked to any source. The sources at the ...
3
votes
5answers
728 views

Is the following two-dimensional graph likely to be globally rigid?

Consider the two-dimensional non-planar graph $G$, with known topology and edge lengths $(r_1, r_2, ... r_N) \in R$, but unknown vertex coordinates. We further specify that: All vertices within a ...