Stretch maps on the affine-additive group
Differential Geometry
2024-11-21 v1 Metric Geometry
Abstract
We define linear and radial stretch maps in the affine-additive group, and prove that they are minimizers of the mean quasiconformal distortion functional. For the proofs we use a method based on the notion of modulus of a curve family and the minimal stretching property (MSP) of the afore-mentioned maps. MSP relies on certain given curve families compatible with the respective geometric settings of the strech maps.
Cite
@article{arxiv.2411.13129,
title = {Stretch maps on the affine-additive group},
author = {Z. M. Balogh and E. Bubani and I. D. Platis},
journal= {arXiv preprint arXiv:2411.13129},
year = {2024}
}
Comments
33 pages, 2 figures