• Corpus ID: 203737260

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

@article{Luckhaus2019StabilityEF,
  title={Stability estimates for the conformal group of \$\mathbb\{S\}^\{n-1\}\$ in dimension \$n\geq 3\$},
  author={Stephan Luckhaus and Konstantinos Zemas},
  journal={arXiv: Differential Geometry},
  year={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 that for a Lipschitz map that is apriori close to a Mobius transformation, an average conformal-isoperimetric type of deficit controls the deviation (in an average sense) of the map in question from a particular Mobius map. The optimality of the result together with its link with the geometric… 

References

SHOWING 1-10 OF 16 REFERENCES
New integral estimates for deformations in terms of their nonlinear strains
AbstractIf u is a bi-Lipschitzian deformation of a bounded Lipschitz domain Ω in ℓn (n≧2), we show that the LP norm (p≧1, p≠n) of a certain “nonlinear strain function” e(u) associated with u
Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
where de denotes normalized surface measure, V is the conformal gradient and q = (2n)/(n 2). A modern folklore theorem is that by taking the infinitedimensional limit of this inequality, one obtains
Geometric Function Theory and Non-linear Analysis
0. Introduction and Overview 1. Conformal Mappings 2. Stability of the Mobius Group 3. Sobolev Theory and Function Spaces 4. The Liouville Theorem 5. Mappings of Finite Distortion 6. Continuity 7.
Stability theorems in geometry and analysis
Foreword to the English Translation. Preface to the First Russian Edition. 1. Introduction. 2. Mobius Transformations. 3. Integral Representations and Estimates for Differentiable Functions. 4.
A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity
The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐limit of
Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences
This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and
Geometric rigidity of conformal matrices
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
Bounds for Deformations in Terms of Average Strains
Rotation and strain
...
...