Chern-Ricci flow on Hermitian minimal models of general type admits uniform estimates yielding subsequential Gromov-Hausdorff convergence under a local Kähler assumption.
Gromov-Hausdorff limits of immortal K\"ahler-Ricci flows
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abstract
We show that the normalized K\"ahler-Ricci flow on a compact K\"ahler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted K\"ahler-Einstein metric on the canonical model, as conjectured by Song-Tian's analytic mimimal model program.
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.