Author

Jun-Bang Liu

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Preprint Sep 2026

Finiteness of null subvarieties and optimal destabilizers for the J-equation

Let $X$ be a compact K\"ahler manifold and $(\alpha,\beta)$ be a pair of K\"ahler classes. We show that when $(\alpha,\beta)$ is $J$-semistable, the collection of positive-dimensional irreducible $J$-null subvarieties is finite. We also obtain a uniform positive lower bound for the normalized $J$-slope of every irreduc...

Jun-Bang Liu · 3 citations

Preprint Aug 2026

The relationship between spacetime singularities and regions at infinity

Ideal attached points are a core concept in general relativity for pseudo-Riemannian manifolds, and whether the spacetime can be extended with certain properties is a central consideration in their choice. This paper establishes a sufficient condition for the separability between singularities and points at infinity fo...

Jun-Bang Liu, Ben Andrews, S. M. Scott · 0 citations

Preprint Aug 2026

The $J$-equation on K\"ahler manifolds under a smooth boundary cone condition

For a $n$-dimensional compact K\"ahler manifold $X$ with a pair of K\"ahler classes $(\alpha,\beta)$, we show that the algebraically defined $J$-null locus is equal to the analytically defined $J$-non-ample locus under the assumption of $J$-bigness(which is automatic for semistable pair up to dimension $3$ \cite{3d}),...

Jun-Bang Liu · 6 citations · ⚡2