https://neckpinch.com/authors/caleb-suan/New arXiv papers by Caleb Suan, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2511.21055arxiv:2511.21055Wed, 26 Nov 2025 00:00:00 GMTSpiro Karigiannis, Sébastien Picard, Caleb Suan — We study flows of G₂-structures guided by the principle of dimensional reduction: natural geometric flows in G₂-geometry reduce to natural flows in complex geometry. Our main examples are the G₂-Laplacian coflow, which lifts the Kähler–Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The G₂-lift of the anomaly flow deforms conformally coclosed G₂-structures. We compare the G₂-anomaly flow to the G₂-Laplacian coflow, and investigate short-time existence and fixed points.Ricci flowKähler–Ricci flowGeneralized & G₂ flows3-manifoldsKähler geometryHarmonic maps & DeTurck trick https://arxiv.org/abs/2406.15254arxiv:2406.15254Fri, 21 Jun 2024 00:00:00 GMTHenrique N. Sá Earp, Julieth Saavedra, Caleb Suan — We explore three versions of the Laplacian coflow of G₂-structures on circle fibrations over Calabi–Yau 3-folds, interpreting their dimensional reductions to the Kähler geometry of the base. Precisely, we reduce Ansätze for the Laplacian coflow, modified or not by de Turck's trick, both on trivial products CY³× S¹ and on contact Calabi–Yau 7-manifolds, obtaining in each case a natural modification of the Kähler–Ricci flow.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–Yau3-manifoldsKähler geometryHarmonic maps & DeTurck trick https://arxiv.org/abs/2209.03411arxiv:2209.03411Wed, 07 Sep 2022 00:00:00 GMTSébastien Picard, Caleb Suan — We establish a correspondence between a parabolic complex Monge-Ampère equation and the G₂-Laplacian flow for initial data produced from a Kähler metric on a complex 2- or 3-fold. By applying estimate for the complex Monge-Ampère equation, we show that for this class of initial data the G₂-Laplacian flow exists for all time and converges to a torsion-free G₂-structure induced by a Kähler Ricci-flat metric. Similar results are obtained for the G₂-Laplacian coflow, and in this case the coflow is related to the Kähler-Ricci flow.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–YauKähler geometryLong-time existence & convergence