https://neckpinch.com/authors/isaac-m-lopez/New arXiv papers by Isaac M. Lopez, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2511.10460/arxiv:2511.10460Thu, 13 Nov 2025 00:00:00 GMTIsaac M. Lopez, Rio Schillmoeller — We introduce a dynamical energy functional on compact ancient asymptotically Ricci-flat Ricci flows with modest decay using limits of conjugate heat flows. This functional satisfies a steady Ricci breather-type rigidity and provides an upper bound for the ordinary λ-functional while retaining many of its properties. In addition, motivated by work of Colding and Minicozzi, we derive local eigenvalue estimates for normalized Ricci flows coupled with conjugate heat flows.Ricci flowAncient solutionsRicci-flat & Calabi–YauHeat kernelStability & uniquenessEigenvalues & spectrum https://neckpinch.com/papers/2407.18438/arxiv:2407.18438Fri, 26 Jul 2024 00:00:00 GMTIsaac M. Lopez, Tristan Ozuch — We classify spin ALE ancient Ricci flows and spin ALE expanding solitons with suitable groups at infinity. In particular, the only spin ancient Ricci flows with groups at infinity in SU(2) and mild decay at infinity are hyperkähler ALE metrics. The main idea of the proof, of independent interest, consists in showing that the large-scale behavior of Perelman's μ-functional on any ALE orbifold with non-negative scalar curvature is controlled by a renormalized λ_ALE-functional related to a notion of weighted mass.Ricci flowRicci solitonsAncient solutionsRicci-flat & Calabi–YauKähler geometryScalar curvature