https://neckpinch.com/authors/joshua-jordan/New arXiv papers by Joshua Jordan, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2004.00785/arxiv:2004.00785Thu, 02 Apr 2020 00:00:00 GMTJoshua Jordan — A fundamental step in the analysis of singularities of Ricci flow was the discovery by Perelman of a monotonic volume quantity which detected shrinking solitons in (arXiv:math/0211159). A similar quantity was found by Feldman, Ilmanen, and Ni in 2005 which detected expanding solitons. The current work introduces a modified length functional as a first step towards a steady soliton monotonicity formula. This length functional generates a distance function in the usual way which is shown to satisfy several differential inequalities which saturate precisely on manifolds satisfying a modification of the steady soliton equation.Ricci flowRicci solitonsSingularities