https://neckpinch.com/authors/kyle-broder/New arXiv papers by Kyle Broder, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2106.13343/arxiv:2106.13343Thu, 24 Jun 2021 00:00:00 GMTKyle Broder — We show that the singularities of the twisted Kähler–Einstein metric arising as the long-time solution of the Kähler–Ricci flow or in the collapsed limit of Ricci-flat Kähler metrics is intimately related to the holomorphic sectional curvature of the reference conical geometry. This provides an alternative proof of the second-order estimate obtained by Gross–Tosatti–Zhang with explicit constants appearing in the divisorial pole.Ricci flowKähler–Ricci flowEinstein metricsRicci-flat & Calabi–YauSingularitiesKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability https://neckpinch.com/papers/2003.14009/arxiv:2003.14009Tue, 31 Mar 2020 00:00:00 GMTKyle Broder — We extend the arguments of Tosatti-Zhang to reduce a well-known conjecture concerning the structure of the Gromov-Hausdorff limit in both the setting of degenerating Calabi-Yau manifolds and the Kähler-Ricci flow to a certain partial second-order estimate.Ricci flowKähler–Ricci flowEinstein metricsRicci-flat & Calabi–Yau(Non)collapsingKähler geometryLimit spaces & RCDKähler–Einstein & K-stability