https://neckpinch.com/authors/roberto-araujo/New arXiv papers by Roberto Araujo, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2507.05097arxiv:2507.05097Mon, 07 Jul 2025 00:00:00 GMTRoberto Araujo — We show that for a broad family of noncompact homogeneous Riemannian manifolds, the corresponding homogeneous Ricci flow solutions have finite extinction time, thereby confirming the dynamical Alekseevskii conjecture for these spaces. As an application, we prove that on such homogeneous manifolds G/H, the space of all G-invariant positive scalar curvature metrics is contractible.Ricci flowScalar curvatureHomogeneous spacesBoundaries & non-compact https://arxiv.org/abs/2312.16517arxiv:2312.16517Wed, 27 Dec 2023 00:00:00 GMTRoberto Araujo — We show that the set of awesome homogeneous metrics on non-compact manifolds is Ricci flow invariant. Moreover, if the universal cover of such awesome homogeneous space is not contractible the Ricci flow has finite extinction time, confirming the Dynamical Alekseevskii Conjecture in this case. We also analyze the long-time limits of awesome homogeneous Ricci flows.Ricci flowHomogeneous spacesBoundaries & non-compactLong-time existence & convergence https://arxiv.org/abs/2310.18182arxiv:2310.18182Fri, 27 Oct 2023 00:00:00 GMTRoberto Araujo — We establish a structure result for the isometry group of non-compact, homogeneous manifolds admitting an immortal homogeneous Ricci flow solution.Ricci flowHomogeneous spacesBoundaries & non-compactLong-time existence & convergence