arXiv subjects
Publications and source records attributed to A. Sukhov.
We solve a problem on filling by Levi-flat hypersurfaces for a class of totally real 2-tori in a real 4-manifold with an almost complex structure tamed by an exact symplectic form. As an application we obtain a simple proof of Gromov's non-squeezing theorem in dimension 4 and new results on rigidity of symplectic structures.
We give a solution to the problem of filling by a Levi-flat hypersurface for a class of totally real tori in C^2 equipped with a certain almost complex structure.
We prove analogs of Thom's transversality theorem and Whitney's theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a manifold.
We consider a multiferroic chain with a linear magnetoelectric coupling induced by the electrostatic screening at the ferroelectric/ferromagnet interface. We study theoretically the dynamic ferroelectric and magnetic response to external magnetic and electric fields by utilizing an approach based on coupled Landau- Khalatnikov and finite-temperature Landau-Lifshitz-Gilbert equations. Additionally, we compare with Monte Carlo calculations. It is demonstrated that for material parameters corresponding to BaTiO3/Fe the polarization and the magnetization are controllable by external magnetic and electric fields respectively.
We prove a result on removing singularities of almost complex structures pulled back by a non-diffeomorphic map. As an application we prove the existence of global J-holomorphic discs with boundaries attached to real tori.
We establish the Schwarz Reflection Principle for $J$-complex discs attached to a real analytic $J$-totally real submanifold of an almost complex manifold with real analytic $J$. We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in $\calc^{k,α}$-classes.
Using the local control theory we derive analytical expressions for magnetic field pulses that steer the magnetization of a monodomain magnetic nanoparticle to a predefined state. Finite-temperature full numerical simulations confirm the analytical results and show that a magnetization switching or freezing is achievable within few precessional periods and that the scheme is exploitable for fast thermal switching.
We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with boundary. As applications we prove a boundary extension and a compactness principle for some elliptic diffeomorphisms between relatively compact domains.
Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E.
We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in $M$ and to give a sufficient condition for the complete hyperbolicity of a domain in $(M,J)$. Finally we obtain the regularity up to the bounday of $J$-holomorphic discs attached to a totally real submanifold in $M$.
We study the compactness of sequences of diffeomorphisms in almost complex manifolds in terms of the direct images of the standard integrable structure.
We propose flow-based analysis to estimate quality of an Internet connection. Using results from the queuing theory we compare two expressions for backbone traffic that have different scopes of applicability. A curve that shows dependence of utilization of a link on a number of active flows in it describes different states of the network. We propose a methodology for plotting such a curve using data received from a Cisco router by NetFlow protocol, determining the working area and the overloading point of the network. Our test is an easy way to find a moment for upgrading the backbone.
We study the problem of holomorphic extension of a smooth CR mapping from a real analytic hypersurface to a real algebraic set in complex spaces of different dimensions.
We establish sufficient conditions for the analyticity of a smooth CR mapping between two real analytic manifolds.