An interpolation theorem on cycle spaces for functions arising as integrals of \(\overline{\partial}\)-closed forms
When \(M\) is a \((k+1)\)-complete complex manifold the space \(C_k(M)\) of compact \(k\)-cycles in \(M\) is Stein. The author proves a precise and quantitative version of this result interpolating, via the integration on \(k\)-cycles of a \((k,k)\) \(\overline\partial\)-closed form on \(M\) with controlled growth, a sequence of values with suitable growth given on a discrete sequence of \(k\)-cycles in \(C_k(M)\). The proof is based on the \(L^2\) method of Andreotti and Vesentini.
\(L^2\) method for \(\overline\partial\)
scientific article; zbMATH DE number 5343274