4 papers · 1 filter
Limiting properties of Hermitian-Einstein metrics under variation of the Kähler class
Nikita Klemyatin
We study the behaviour of Hermitian-Einstein metrics on a holomorphic vector bundle over a compact Kähler manifold, as the underlying Kähler metric varies and its Kähler class chan…
Convergence of the inverse Monge-Ampere flow and Nadel multiplier ideal sheaves
Nikita Klemyatin
We generalize the inverse Monge-Ampere flow, which was introduced in \cite{CHT17}, and provide conditions that guarantee the convergence of the flow without a priori assumption tha…
Convergence of Type IIA manifolds and application to the Type IIA flow
Nikita Klemyatin
The Type IIA flow is a flow of 3-forms on a 6-dimensional symplectic manifold. It was introduced by Fei, Phong, Picard, and Zhang in \cite{FPPZb}. There is little known about the s…
Convergence of Hermitian manifolds and the Type IIB flow
Nikita Klemyatin
The Type IIB flow is a flow of conformally balanced complex manifolds introduced by Phong, Picard, and Zhang, about whose singularities little is as yet known. We formulate converg…