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Results tagged with rigidity
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user 1441
1
vote
Constant Gaussian curvature disks
The answer is yes.
Since curvature is 1, there is an isometric immersion $\iota\colon D\looparrowright \mathbb{S}^2$. Note that the curve $\iota(\partial D)$ has constant curvature, therefore $\iota(\ …
- 45k
3
votes
How to correctly state Cauchy's rigidity theorem?
Yes, formally speaking the statement is incorrect.
The correct assumption is: there is a continuous bijection between the surfaces of two polyhedra that maps each facet to a facet by isometry.
Alexand …
- 45k