Geodesic
Second-order estimates for collapsed limits of Ricci-flat Kähler metrics
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 912-926

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DOI

We show that the singularities of the twisted Kähler–Einstein metric arising as the longtime solution of the Kähler–Ricci flow or in the collapsed limit of Ricci-flat Kähler metrics are intimately related to the holomorphic sectional curvature of reference conical geometry. This provides an alternative proof of the second-order estimate obtained by Gross, Tosatti, and Zhang (2020, Preprint, arXiv:1911.07315) with explicit constants appearing in the divisorial pole.
DOI : 10.4153/S0008439522000765
Mots-clés : Calabi–Yau manifolds, Kähler metrics, collapsed geometry, Kähler–Ricci flow, holomorphic sectional curvature, Schwarz lemma 
Broder, Kyle. Second-order estimates for collapsed limits of Ricci-flat Kähler metrics. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 912-926. doi: 10.4153/S0008439522000765
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     author = {Broder, Kyle},
     title = {Second-order estimates for collapsed limits of {Ricci-flat} {K\"ahler} metrics},
     journal = {Canadian mathematical bulletin},
     pages = {912--926},
     year = {2023},
     volume = {66},
     number = {3},
     doi = {10.4153/S0008439522000765},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000765/}
}
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