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math.DG2026
Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces
Tongxin Xu, Zhenlei Zhang
We prove that any finite time collapsing Kähler Ricci flow on ruled surfaces develops a Type I singularity, such singularity is modeled on the standard product shrinker $\mathbb{P}…
math.DG2026
Finite Time Type I Singularities of the Kähler Ricci Flow
Tongxin Xu, Zhenlei Zhang
We prove the Feldman--Ilmanen--Knopf conjecture for finite time Type I singularities of the Kähler--Ricci flow. More precisely, for any compact Kähler manifold and its blow-up…
math.DG2026
Compactness and Rigidity of Complete Kähler Ricci Shrinkers
Tongxin Xu, Zhenlei Zhang
In this paper, we study compactness, rigidity, and related geometric properties of complete Kähler Ricci shrinkers through the polarized Fano fibration structure.