STRATIFIED ELLIPTIC ESTIMATES AND STRONG CONVERGENCE OF L^2 -HARMONIC FORMS ON COMPLEX VARIETIES WITH ISOLATED SINGULARITIES

Let $V$ be a compact irreducible complex analytic space with isolated singularities $\Sigma$, and let$V'=V\setminus\Sigma$. We study a singular-limit problem for a degenerating family of completeHodge--de~Rham complexes on $V'$ in Ohsawa's isolated-singularity setting and prove adomain-stability theorem for this degeneration. After transporting the varying $\Ltwo$ spaces to afixed Hilbert space, we establish a fixed-space variational lower-semicontinuity statement togetherwith the local compactness needed to extract subsequential strong local limits on compact subsets of $V'$.For normalized $\Ltwo$-harmonic forms, we show that every such subsequential limit lies in theminimal closed extension associated with the limiting incomplete metric. The proof combines$\varepsilon$-uniform stratified elliptic estimates, local compactness, a one-sided variationallower-semicontinuity argument at the maximal level, and a logarithmic cutoff argument eliminatingresidual boundary data at the singular points. This yields a reusable functional-analytic mechanismfor singular Hodge degeneration. As a first application, we recover the correspondence betweenreduced minimal $\Ltwo$ de~Rham cohomology and intersection cohomology for compact complex analyticspaces with isolated singularities. When combined with Ohsawa's separate topological invariance inputfor the reduced $\Ltwo$ cohomology of the complete family, the same framework also yields stabilityof harmonic dimensions along that family.