相关论文: Quasianalyticity and pluripolarity

This is a survey of results, both classical and recent, on behaviour of plurisubharmonic functions near their $-\infty$-points, together with the related topics for positive closed currents.

We study the functional equation $A\circ X=X\circ B$, where $A,$ $B$, and $X$ are polynomials over $\mathbb C$. Using previous results of the author about polynomials sharing preimages of compact sets, we show that for given $B$ its…

We extend the characterization of context-free groups of Muller and Schupp in two ways. We first show that for a quasi-transitive inverse graph $\Gamma$, being quasi-isometric to a tree, or context-free (finitely many end-cones types), or…

A $biased\ graph$ is a pair $(G,\mathcal{B})$, where $G$ is a graph and $\mathcal{B}$ is a collection of `balanced' circuits of $G$ such that no $\Theta$-subgraph of $G$ contains precisely two balanced circuits. We prove a Ramsey-type…

Using the stratifications of Deligne-Mumford moduli spaces $\overline{\mathcal M}_{g,n}$ indexed by stable graphs, we introduce a partially ordered set of stable graphs by defining a partial ordering on the set of connected stable graphs of…

The $L^{p,\infty}$ quasi-norm of functions on a measure space can be characterized in terms of their pairing with normalized characteristic functions. We generalize this result to the case of the outer $L^{p,\infty}$ quasi-norms for…

We consider complex Henon maps which are quasi-hyperbolic. We show that a quasi-hyperbolic map is uniformly hyperbolic if and only if there are no tangencies between stable and unstable manifolds.

We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex.…

The paper consider an equivalence relation in the set of vertices of a bipartite graph. Some numerical characteristics showing the cardinality of equivalence classes are introduced. A combinatorial identity that is in relationship to these…

We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.

A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…

In this paper we study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.

In [1, 2, 3] the Corolla Polynomial $ \mathcal C (\Gamma) \in \mathbb C [a_{h_1}, \ldots, a_{h_{\left \vert \Gamma^{[1/2]} \right \vert}}] $ was introduced as a graph polynomial in half-edge variables $ \left \{ a_h \right \} _{h \in…

We show that the dual graph of the triangulation of the flow polytope of the zigzag graph adorned with the length-reverse-length framing is a subgraph of a grid graph. Through M\'esz\'aros, Morales, and Striker's bijection between simplices…

We consider inclusions of type $(P\otimes A)^G\subset(P\otimes B)^G$, where $G$ is a compact quantum group of Kac type acting on a ${\rm II}_1$ factor $P$, and on a Markov inclusion of finite dimensional $C^*$-algebras $A\subset B$. In the…

For a class of symplectic manifolds, we introduce a functional which assigns a real number to any pair of continuous functions on the manifold. This functional has a number of interesting properties. On the one hand, it is Lipschitz with…

A simple graph $G$ with maximum degree $\Delta$ is \emph{overfull} if $|E(G)|>\Delta \lfloor |V(G)|/2\rfloor$. The \emph{core} of $G$, denoted $G_{\Delta}$, is the subgraph of $G$ induced by its vertices of degree $\Delta$. Clearly, the…

Let $S$ be a compact oriented surface. We construct homogeneous quasimorphisms on $Diff(S, area)$, on $Diff_0(S, area)$ and on $Ham(S)$ generalizing the constructions of Gambaudo-Ghys and Polterovich. We prove that there are infinitely many…

It is a classical fact that the number of vertices of the graphical zonotope $Z_\Gamma$ is equal to the number of acyclic orientations of a graph $\Gamma$. We show that the $f$-polynomial of $Z_\Gamma$ is obtained as the principal…

As an absolute invariant of smooth conjugacy, the multiplier group described the types of space-time symmetries that the flow has, and for a quasiperiodic flow on the $n$-torus, is the determining factor of the structure of its generalized…