The curve-lengthening flow in inversive geometry
Differential Geometry
2025-02-26 v1 Analysis of PDEs
Abstract
We consider an invariant gradient flow for the invariant length functional for co-compact curves in inversive geometry, and prove that solutions exist for all time and converge to loxodromic curves, provided the initial curve is admissible (so that the invariant length element is well defined).
Cite
@article{arxiv.2502.17896,
title = {The curve-lengthening flow in inversive geometry},
author = {Ben Andrews and Glen Wheeler},
journal= {arXiv preprint arXiv:2502.17896},
year = {2025}
}
Comments
18 pages, 3 figures