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arXiv · 2503.18392

$L^1$-Stability for complex Monge-Amp\`ere equations

Songchen Liu·Liyou Zhang
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Abstract

We first establish the weak stability results for solutions of complex Monge-Amp\`ere equations in relative full mass classes, extending the results known to hold in the full mass class. Building on weak stability, we then prove the $\mathcal{C}^{k,\alpha}$ stability of solutions to complex Monge-Amp\`ere equations on quasi-projective varieties. As an application, we study the limit of the singular Ricci-flat metrics on $\mathbb{Q}$-Calabi-Yau projective varieties, inspired by Tosatti's work on Calabi-Yau projective manifolds.

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BibTeXRIS

Songchen Liu, Liyou Zhang. 2025-03-24. $L^1$-Stability for complex Monge-Amp\`ere equations. https://arxiv.org/abs/2503.18392

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