English

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).

Keywords

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

R2 v1 2026-06-28T21:56:49.865Z