arXiv subjects

Caleb Suan

Publications and source records attributed to Caleb Suan.

5 recordsLinked to original sources

arXiv2026

Flows of conformally coclosed $G_2$-structures with dilaton

We study flows of $G_2$-structures guided by the principle of dimensional reduction: natural geometric flows in $G_2$-geometry reduce to natural flows in complex geometry. Our main examples are the $G_2$-Laplacian coflow, which lifts the Kähler--Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The $G_2$-lift of the anomaly flow deforms conformally coclosed $G_2$-structures. We compare the $G_2$-anomaly flow to the $G_2$-Laplacian coflow, and investigate short-time existence and fixed points.

math.DG↗

arXiv2025

Gromov-Hausdorff continuity of non-Kähler Calabi-Yau conifold transitions

We study the geometry of Calabi-Yau conifold transitions. This deformation process is known to possibly connect a Kähler threefold to a non-Kähler threefold. We use balanced and Hermitian-Yang-Mills metrics to geometrize the conifold transition and show that the whole operation is continuous in the Gromov-Hausdorff topology.

math.DG↗

arXiv2025

Laplacian coflows of $G_2$-structures on contact Calabi--Yau 7-manifolds

We explore three versions of the Laplacian coflow of $G_2$-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 $CY^3\times S^1$ and on contact Calabi--Yau 7-manifolds, obtaining in each case a natural modification of the Kähler--Ricci flow.

math.DG↗

arXiv2024

Anomaly Flow: Shi-Type Estimates and Long-time Existence

We consider the long-time existence of the anomaly flow on a compact complex $3$-fold with general slope parameter $α'$. In particular, we obtain integral Shi-type estimates for the flow by adapting a integration-by-parts type argument instead of the usual maximum principle techniques. Following this, we prescribe a sufficient smallness condition on $α'$ in order to extend the flow on $[0,τ)$ to $[0,τ+ ε)$.

math.DG↗

arXiv2023

Flows of $G_2$-Structures associated to Calabi-Yau Manifolds

We establish a correspondence between a parabolic complex Monge-Ampère equation and the $G_2$-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 $G_2$-Laplacian flow exists for all time and converges to a torsion-free $G_2$-structure induced by a Kähler Ricci-flat metric. Similar results are obtained for the $G_2$-Laplacian coflow, and in this case the coflow is related to the Kähler-Ricci flow.

math.DG↗