https://neckpinch.com/authors/hollis-williams/New arXiv papers by Hollis Williams, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2404.13063/arxiv:2404.13063Fri, 12 Apr 2024 00:00:00 GMTHollis Williams — We study the behavior of the Cheeger isoperimetric constant under the Ricci flow on compact surfaces. For metrics on a surface diffeomorphic to S², we show that the Cheeger constant is non-decreasing along the flow. The proof uses evolution identities for parallel curves together with a viscosity formulation of the evolution of log h which accommodates for the possible switching of minimizing regions. We also give examples of nontrivial Ricci flows on topological 2-spheres for which the Cheeger constant remains constant, demonstrating that strict monotonicity is not expected.Ricci flowSurfacesGeometric inequalities