Chern-Ricci flow on Hermitian minimal models of general type admits uniform estimates yielding subsequential Gromov-Hausdorff convergence under a local Kähler assumption.
Gill, The Chern-Ricci flow on smooth minimal models of general type
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abstract
We show that on a smooth Hermitian minimal model of general type the Chern-Ricci flow converges to a closed positive current on M. Moreover, the flow converges smoothly to a Kahler-Einstein metric on compact sets away from the null locus of K_M. This generalizes work of Tsuji and Tian-Zhang to Hermitian manifolds, providing further evidence that the Chern-Ricci flow is a natural generalization of the Kahler-Ricci flow.
fields
math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves diameter estimates, volume non-collapsing, and Gromov-Hausdorff convergence for normalized Chern-Ricci flow on complex minimal surfaces of general type from arbitrary Hermitian metrics.
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Gromov-Hausdorff limits of the Chern-Ricci flow on smooth Hermitian minimal models of general type
Chern-Ricci flow on Hermitian minimal models of general type admits uniform estimates yielding subsequential Gromov-Hausdorff convergence under a local Kähler assumption.
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Convergence of the Chern-Ricci flow on complex minimal surfaces of general type
Proves diameter estimates, volume non-collapsing, and Gromov-Hausdorff convergence for normalized Chern-Ricci flow on complex minimal surfaces of general type from arbitrary Hermitian metrics.