Normalized Kähler-Ricci flow converges in Gromov-Hausdorff sense to the metric completion of the twisted Kähler-Einstein metric on the canonical model when the canonical bundle is semiample.
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math.DG 5years
2026 5verdicts
UNVERDICTED 5representative citing papers
Chern-Ricci flow on Hermitian minimal models of general type admits uniform estimates yielding subsequential Gromov-Hausdorff convergence under a local Kähler assumption.
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.
Exact asymptotic rates for small Laplacian eigenvalues on degenerations of compact Kähler manifolds are derived, generalizing Dai-Yoshikawa to higher dimensions via Skoda inequality and auxiliary Monge-Ampère equations.
Proves optimal Sobolev inequalities and local volume noncollapsing for compact Kähler manifolds with bounded q-Nash entropy.
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Gromov-Hausdorff limits of immortal K\"ahler-Ricci flows
Normalized Kähler-Ricci flow converges in Gromov-Hausdorff sense to the metric completion of the twisted Kähler-Einstein metric on the canonical model when the canonical bundle is semiample.
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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.
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Asymptotics of small eigenvalues on degenerations of K\"ahler manifolds
Exact asymptotic rates for small Laplacian eigenvalues on degenerations of compact Kähler manifolds are derived, generalizing Dai-Yoshikawa to higher dimensions via Skoda inequality and auxiliary Monge-Ampère equations.
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Optimal geometric estimates for compact K\"ahler manifolds of a Nash entropy bound
Proves optimal Sobolev inequalities and local volume noncollapsing for compact Kähler manifolds with bounded q-Nash entropy.