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math.DG2025
Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
Ronan J. Conlon, Tran-Trung Nghiem
We present infinitely many new examples of affine Calabi--Yau manifolds of Euclidean volume growth and quadratic curvature decay, whose tangent cones at infinity are irregular and…
math.DG2024
Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity
Tran-Trung Nghiem
We show that on every non- complex symmetric space of rank two, there are complete Calabi-Yau metrics of Euclidean volume growth with prescribed horospherical singular tangent…
math.DG2022
On the regularity of conical Calabi-Yau potentials
Tran-Trung Nghiem
Using pluripotential theory on degenerate Sasakian manifolds, we show that a locally bounded conical Calabi-Yau potential on a Fano cone is actually smooth on the regular locus. Th…