相关论文: An answer to a question of Herman, Baker and Rippo…

Using McMullen's rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk.

Let P be a locally finite disk pattern on the complex plane C whose combinatorics are described by the one-skeleton G of a triangulation of the open topological disk and whose dihedral angles are equal to a function \Theta:E\to [0,\pi/2] on…

Let f be an entire function with a bounded set of singular values, and suppose furthermore that the postsingular set of f is bounded. We show that every component of the escaping set I(f) is unbounded. This provides a partial answer to a…

We prove `polynomial in $k$' bounds on the size of the Bergman kernel for the space of holomorphic Siegel cusp forms of degree $n$ and weight $k$. When $n=1,2$ our bounds agree with the conjectural bounds on the aforementioned size, while…

Let $D$ be a closed disk centered at the origin in the horizontal hyperplane $\{t=0\}$ of the sub-Riemannian Heisenberg group $\hh^n$, and $C$ the vertical cylinder over $D$. We prove that any finite perimeter set $E$ such that $D\subset…

We study a family of initial boundary value problems associated to mixed hyperbolic-parabolic systems: v^{\epsilon} _t + A (v^{\epsilon}, \epsilon v^{\epsilon}_x ) v^{\epsilon}_x = \epsilon B (v^{\epsilon} ) v^{\epsilon}_{xx} The…

This paper is mainly concerned with the disk of convergence of a power series s(x) representing an algebraic function of x and specifically with the relation between this disk and the branch points of the function. We shall focus especially…

S. Baker (2019), B. B\'ar\'any and A. K\"{a}enm\"{a}ki (2019) independently showed that there exist iterated function systems without exact overlaps and there are super-exponentially close cylinders at all small levels. We adapt the method…

We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…

We show that if $F(s)$ is a nondegenerate ordinary Dirichlet series with nonnegative coefficients and $F(k)$ is a rational number for all large enough positive integers $k$, then the denominators of those rational numbers are unbounded. In…

Based on the weak expansion property of a long iteration of a family of quasi-Blaschke products near the unit circle established recently, we prove that the Julia sets of a number of transcendental entire functions with bounded type Siegel…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

We call every complex connected (1,1)-dimensional supermanifold a super Riemann surface and construct versal super families of compact ones, where the base spaces are allowed to be certain ringed spaces including all complex supermanifolds.…

We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the…

For a complete Riemannian manifold with bounded geometry, we prove the existence of isoperimetric clusters and also the compactness theorem for sequence of clusters in a larger space obtained by adding finitely many limit manifolds at…

In 2008 Petersen posed a list of questions on the application of trans-quasiconformal Siegel surgery developed by Zakeri and himself. In this paper we extend Petersen-Zakeri's idea so that the surgery can be applied to all the premodels…

Let $L$ be a compact oriented Lagrangian surface in a K\"ahler surface endowed with a complete Riemannian metric (compatible with the symplectic structure and the complex structure) with bounded sectional curvatures and a positive lower…

We show that sequences of positive integers whose ratios $a_n^2/a_{n+1}$ lie within a specific range are almost uniquely determined by their reciprocal sums. For instance, the Sylvester sequence is uniquely characterized as the only…

We show that there exists a bounded subset of R such that no system of exponentials can be a Riesz basis for the corresponding Hilbert space. An additional result gives a lower bound for the Riesz constant of any putative Riesz basis of the…

We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our…