3 papers
math.AG2026
K-semistability and singularities of normal affine cones
Tran-Trung Nghiem
We provide a complete and optimal characterization of -Gorenstein normal affine singularities in terms of their K-stability in the sense of Collins--Székelyhidi.
math.DG2025
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.DG2025
Examples of complete Calabi--Yau metrics on affine smoothings of irregular toric Calabi--Yau cones
Ronan J. Conlon, Tran-Trung Nghiem
We present new examples of affine Calabi--Yau manifolds of Euclidean volume growth and quadratic curvature decay, whose tangent cones at infinity are irregular and have smooth link…