arXiv subjects

Nikita Klemyatin

Publications and source records attributed to Nikita Klemyatin.

6 recordsLinked to original sources

arXiv2025

Convergence of the inverse Monge-Ampere flow and Nadel multiplier ideal sheaves

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 that $X$ has a Kähler-Einstein metric. We also show that if the underlying manifold does not admit Kähler-Einstein metric, then the flow develops Nadel multiplier ideal sheaves. In addition, we establish the linear lower bound for $\inf_Xφ$, and the theorem of Darvas and He for the inverse Monge-Ampere flow.

math.DG↗

arXiv2023

On uniform estimates for $(n-1)-$form fully nonlinear partial differential equations on compact Hermitian manifolds

We obtain a priori $L^\infty$ estimate for a general class of $(n-1)-$form fully nonlinear partial differential equations on compact Hermitian manifolds. Our method relies on the local version of comparison with auxiliary Monge-Ampère equations, developed earlier by B. Guo and D. H. Phong. The key is to find the appropriate elliptic operator such that the maximum principle applies.

math.AP↗

arXiv2022

Convergence of Type IIA manifolds and application to the Type IIA flow

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 singularities of this flow in general. We formulate and prove convergence theorems for this flow. We also describe the singularity models for this flow.

math.DG↗

arXiv2021

Convergence of Hermitian manifolds and the Type IIB flow

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 convergence criteria for the Gromov-Cheeger-Hamilton convergence of sequences of Hermitian manifolds, and apply them to precompactness theorems and the existence of singularity models for the Type IIB flow, in analogy with Hamilton's classic compactness theorems and classification of singularities for the Ricci flow.

math.DG↗

arXiv2019

Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group

Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute the Dolbeault cohomology of Vaisman manifolds.

math.AG↗

arXiv2019

Universal spaces of parameters for complex Grassmann manifolds $G_{q+1,2}$

Buchstaber and Terzic introduced a notion of universal space of parameters $\mathcal{F}$ for a manifold $M^{2n}$, which has an effective action of compact torus $T^k$ , $k \leq n$ with some additional properties. with special properties. This space is needed to construction of factor $M^{2n}/T^k$. Buchstaber and Terzic constructed the universal space of parameters for $G_{5,2}$. In this work we construct universal space of parameters for complex Grassmann manifold $G_{q+1,2}$. Our construction is based on the construction of moduli space of stable curves of genus zero with $q+1$ marked points due to Salamon, McDuff and Hofer.

math.AT↗