2025/03/24 by Liu, Songchen, Zhang, Liyou
#32J17 #32Q20 #32U15 #32W20 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.18392
We first establish the weak stability results for solutions of complex Monge-Ampère 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 Ck,α stability of solutions to complex Monge-Ampère equations on quasi-projective varieties. As an application, we study the limit of the singular Ricci-flat metrics on ℚ-Calabi-Yau projective varieties, inspired by Tosatti's work on Calabi-Yau projective manifolds.