Extensions with estimates of cohomology classes

TL;DR

This paper extends the Ohsawa-Takegoshi theorem to Dolbeault cohomology classes on hypersurfaces in Kähler manifolds, providing new tools for complex geometry and cohomology extension problems.

Contribution

It introduces an extension theorem for Dolbeault q-classes, broadening the scope of cohomology class extension in complex geometry.

Findings

Proves an Ohsawa-Takegoshi type extension theorem for Dolbeault q-classes

Applicable to smooth compact hypersurfaces in weakly pseudoconvex Kähler manifolds

Advances understanding of cohomology class extensions in complex geometry

Abstract

We prove an extension theorem of "Ohsawa-Takegoshi type" for Dolbeault q$-classes of cohomology ($q\geq 1$) on smooth compact hypersurfaces in a weakly pseudoconvex K\"ahler manifold