Questions tagged [rigidity]

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Definition of a uniformly bounded dual of a group

The unitary dual of a group $G$ is the set of equivalence classes of irreducible unitary representations of $G$ with the Fell topology. (This topology is defined using convergence of positive definite ...
9
votes
0answers
160 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 ...
4
votes
0answers
76 views

Conformal $L^p$ rigidity of Riemannian manifolds

$\newcommand{\M}{\mathcal{M}}$ $\newcommand{\N}{\mathcal{N}}$ $\newcommand{\R}{\mathbb{R}}$ $\newcommand{\CO}[1]{\text{CO}(#1)}$ $\newcommand{\dist}{\operatorname{dist}}$ $\newcommand{\g}{\mathfrak{g}}...
3
votes
0answers
146 views

Rigidity vs Super-rigidity of representations (of Kähler/surface groups)

In the literature there are several definitions of "rigidity" (or "super-rigidity") of representations, adapted to the circumastances. I wonder what are the relations between them; I excuse in advance ...
2
votes
0answers
94 views

$l$-adic rigidity for Milnor $K$-theory

Given a local henselian ring $A$ with the maximal ideal $m$, does the quotient map $A\mapsto A/m$ induce isomorphisms on $l$-adic Milnor $K$-theories? ($K_n^M(R)\otimes \mathbb{Z}_l$, where $l$ is an ...
2
votes
0answers
54 views

Infinitesimal rigidity vs local rigidity of isometrically immersed riemannian manifolds

I was reading the nice survey on rigidity, focusing on tensegrities by Connelly, and I'd like to know the status and feedback about a question he asks: A theorem by Gluck and this work of Connelly, ...
2
votes
0answers
72 views

Are a map with constant singular values and its inverse always conjugate through isometries?

Let $U \subseteq \mathbb R^2$ be open, connected and bounded, and let $0<\sigma_1<\sigma_2$ satisfy $\sigma_1 \sigma_2=1$. Suppose that $f:U \to U$ is a diffeomorphism whose singular values (of $...
2
votes
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218 views

Rigidity of Diophantine torus translations

Let $T_a:x\mapsto x+a$ be a Diophantine translation on the torus $\mathbb T^d$, $d>1$. Let $h$ be some $C^1$ diffeomorphism of $\mathbb T^d$ such that $$ g=h\circ T_a\circ h^{-1} $$ is $C^\infty$. ...