ScalingStacks

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Remark 4.9. The $s$ -dependence is probably not optimal.

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In this chapter

Chapter overview

1 Introduction
2 Analytic backgrounds
2.1 Skoda inequality
2.2 Kolodziej’s estimate on pluripotentials
2.3 Algebraic metrics and asymptotes
2.4 Extension of Kähler currents
2.5 Savin’s small perturbation theorem
2.6 Regularity theory for real Monge-Ampère
2.7 Special Lagrangian fibration
3 Degenerating Calabi-Yau hypersurfaces
3.1 Complex structure
3.2 Piecewise linear structure
3.3 Kählerian polarisation
3.4 Extension property and locally convex functions
3.5 Extension property: the Fermat case
4 Estimates on the Kähler potential
4.1 Harnack inequality
4.2 Local potentials: convexity
4.3 Local potentials: plurisubharmonicity
4.4 Locally convex function
4.5 Legendre transform, extension, regularisation
4.6 Improved Skoda inequality
4.7 $L^{\infty}$ and stability estimates for CY potentials
5 Fermat case: Metric convergence and SYZ fibration
5.1 Limiting real MA metric
5.2 Higher regularity in the generic region
5.3 Gromov-Hausdorff convergence
5.4 Special Lagrangian fibration in the generic region
References

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