2025 Theses Doctoral

On the singularities of the Type IIA flow, the Type IIB flow and the inverse Monge-Ampere flow

Klemyatin, Nikita

We study the singularity formation of Type IIA and Type IIB flows. These flows were introduced by Fei, Phong, Picard, and Zhang in [1,2,3]. We establish and prove convergence theorems for these flow and describe the singularity models associated with it.

We also study the inverse Monge-Ampère flow on compact Kähler manifolds. We provide conditions that ensure its convergence, show that if the underlying manifold does not admit a Kähler-Einstein metric, the flow develops Nadel multiplier ideal sheaves, and establish a linear lower bound for inf_𝜘𝜙.