# Geometric rigidity of conformal matrices

@article{Faraco2005GeometricRO, title={Geometric rigidity of conformal matrices}, author={Daniel Faraco and Xiao Zhong}, journal={Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze}, year={2005}, volume={4}, pages={557-586} }

We provide a geometric rigidity estimate a la Friesecke-James-Muller for conformal matrices. Namely, we replace SO(n) by a arbitrary compact subset of conformal matrices, bounded away from 0 and invariant under SO(n), and rigid motions by Mobius transformations.

## 23 Citations

Stability estimates for the conformal group of S^(n-1} in dimension n >= 3

- Mathematics
- 2019

The purpose of this paper is to exhibit a quantitative stability result for the class of Möbius transformations of Sn−1 when n ≥ 3. The main estimate is of local nature and asserts that for a…

Integral Estimates for Approximations by Volume Preserving Maps

- Mathematics
- 2017

A quantitative Brenier decomposition shows that the deviation of a map from volume preserving is bounded by the deviation of the derivative from volume preserving. A study of the matrix nearness…

On multiwell Liouville theorems in higher dimension

- Mathematics
- 2008

Abstract. We consider certain subsets of the space of matrices of the form and we prove that for , and for connected , there exists a positive constant depending on such that for we have provided u…

A TWO WELL LIOUVILLE THEOREM

- Mathematics
- 2005

In this paper we analyse the structure of approximate solutions to the compatible two well problem with the constraint that the surface energy of the solution is less than some fixed constant. We…

Improved bounds for composites and rigidity of gradient fields

- Computer Science, MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2007

An improved lower bound for the conductivity of three-component composite materials is determined using a new quantitative rigidity estimate for gradient fields in two dimensions.

Stability estimates for the conformal group of $\mathbb{S}^{n-1}$ in dimension $n\geq 3$

- Mathematics
- 2019

The purpose of this paper is to exhibit a quantitative stability result for the class of Mobius transformations of $\mathbb{S}^{n-1}$ when $n\geq 3$. The main estimate is of local nature and asserts…

Weighted generalized Korn inequality on John domains

- Mathematics
- 2016

The goal of this work is to show that the generalized Korn inequality that replaces the symmetric part of the differential matrix in the classical Korn inequality by its trace-free part is valid over…

L ∞-Extremal Mappings in AMLE and Teichmüller Theory

- Mathematics
- 2014

These lecture focus on two vector-valued extremal problems which have a common feature in that the corresponding energy functionals involve L ∞ norm of an energy density rather than the more familiar…

Korn-Type Inequalities in Orlicz-Sobolev Spaces Involving the Trace-Free Part of the Symmetric Gradient and Applications to Regularity Theory

- Mathematics
- 2012

We prove variants of Korn’s inequality involving the trace-free part of the symmetric gradient of vector fields v : Ω→ Rn (Ω ⊂ Rn), that is, ˆ

Weighted generalized Korn inequalities on John domains

- MathematicsMathematical Methods in the Applied Sciences
- 2018

The goal of this work is to show that the generalized Korn inequality that replaces the symmetric part of the differential matrix in the classical Korn inequality by its trace‐free part is valid over…

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