Communications in Analysis and Geometry
Volume 28 (2020)
A new geometric flow over Kähler manifolds
Pages: 1251 – 1288
In this paper, we introduce a geometric flow for Kähler metrics $\omega_t$ coupled with closed $(1,1)$‑forms $\alpha_t$ on a compact Kähler manifold, whose stationary solution is a constant scalar curvature Kähler (cscK) metric, coupled with a harmonic $(1,1)$‑form. We establish the long-time existence, i.e., assuming the initial $(1,1)$‑form $\alpha$ is nonnegative, then the flow exists as long as the norm of the Riemannian curvature tensors are bounded.
The first author is supported in part by the Fonds National de la Recherche Luxembourg (FNR) under the OPEN scheme (project GEOMREV O14/7628746); the second author is supported in part by NSF grant DMS-1412384; and the third author is supported in part by the Simons Foundation’s program: Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics.
Received 15 October 2015
Accepted 5 February 2018
Published 2 December 2020