Unbounded locus of the weak J-equation solution

Determine the unbounded locus of the normalized weak solution of the semistable J-equation on a compact Kähler manifold.

Background

For a numerically J-semistable pair of Kähler classes, the paper proves that Murakami’s normalized weak solution is smooth outside the numerical J-null locus and identifies that null locus with the ambient C^2-singular locus. These results establish local boundedness away from the null locus, but they do not determine where the solution itself is unbounded.

The unresolved issue is to characterize the global unbounded locus of the normalized weak solution, including its relationship to the numerical J-null locus and the singularities of the associated weak solution. The paper later notes that global boundedness is known under an additional smooth boundary-cone subsolution assumption, but not under numerical semistability alone.