https://neckpinch.com/authors/francesco-pediconi/New arXiv papers by Francesco Pediconi, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.16743arxiv:2608.16743Mon, 17 Aug 2026 00:00:00 GMTAlessandro Goffi, Francesco Pediconi — We study higher-order global estimates for the heat equation on Riemannian manifolds, both for static metrics and for metrics evolving under the Ricci flow. Under minimal geometric assumptions, we derive first-order regularizing estimates for log-solutions of the heat equation, together with upper second-order bounds with explicit constants. Our quantitative approach is based on integral duality methods proposed by L.\ C.\ Evans, J.-M.\ Lasry and P.-L.\ Lions in different settings.Ricci flow https://arxiv.org/abs/2602.15661arxiv:2602.15661Tue, 17 Feb 2026 00:00:00 GMTAnusha M. Krishnan, Francesco Pediconi — We prove a precompactness theorem for invariant metrics on compact homogeneous spaces without injectivity radius bounds, assuming uniform bounds on the diameter and on all derivatives of the curvature tensor. As a consequence, we prove that every ancient homogeneous Ricci flow on a compact manifold admits a blow-down sequence that converges to a gradient shrinking Ricci soliton.Ricci flowRicci solitonsAncient solutionsLimit spaces & RCDHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2312.01469arxiv:2312.01469Sun, 03 Dec 2023 00:00:00 GMTAnusha M. Krishnan, Francesco Pediconi, Sammy Sbiti — Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarantees flowing through diagonal metrics and a tameness assumption on the collapsing directions, we prove that such solutions have additional symmetries, i.e., they are invariant under the right action of their collapsing torus. As a byproduct of these additional torus symmetries, we prove that these solutions converge, backward in time, in the Gromov-Hausdorff topology to an Einstein metric on the base of a torus bundle.Ricci flowAncient solutionsEinstein metrics(Non)collapsingLimit spaces & RCDHomogeneous spaces https://arxiv.org/abs/2110.05818arxiv:2110.05818Tue, 12 Oct 2021 00:00:00 GMTFrancesco Pediconi, Sammy Sbiti — We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov-Hausdorff topology, under a suitable rescaling, to an Einstein metric on the base of a torus fibration. This construction generalizes all previous known examples in the literature.Ricci flowAncient solutionsEinstein metricsLimit spaces & RCDHomogeneous spaces