3 papers
math.AG2026
Logarithmic -lemma and several geometric applications (with an Appendix joint with Sheng Rao)
Runze Zhang
In this paper, we prove a -type lemma on compact Kähler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line…
math.CV2025
On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) -Kähler structures
Sheng Rao, Runze Zhang
Inspired by a recent work of D. Wei--S. Zhu on the extension of closed complex differential forms and Voisin's usage of the -lemma, we obtain several new th…
math.DS2025
Parabolic Implosion in the Parameter Space of Cubic Polynomials
Runze Zhang
Parabolic implosion describes the enrichment of Julia sets when a parabolic fixed point is perturbed. It is also natural to study parabolic implosion in parameter spaces. In partic…