Automorphism groups of domains that depend on fewer than the maximal number of parameters

Exponential mixing property for automorphisms of compact Kähler manifolds

Let $f$ be a holomorphic automorphism of a compact Kähler manifold. Assume moreover that $f$ admits a unique maximal dynamic degree $d_p$ with only one eigenvalue of maximal modulus. Let $μ$ be its equilibrium measure. In this paper, we prove that $μ$ is exponentially mixing for all d.s.h.\ test functions.

Sur les automorphismes reguliers de C^k

We show the uniqueness for the measure of maximal entropy for regular automorphisms of C^k.

由最大模诱导的单位开盘解析自同构群上的右不变度量

The right invariant metric on the analytic automorphism group of the unit open disk induced by maximal modulus

本文研究由最大模诱导的单位开盘解析自同构群上的右不变度量，推导了该度量的显式公式，并刻画了其近正则Finsler几何结构。

Distinguished Line Bundles for Complex Surface Automorphisms

We equate dynamical properties (e.g., positive entropy, existence of a periodic curve) of complex projective surface automorphisms with properties of the pull-back actions of such automorphisms on line bundles. We use the properties of the cohomological actions to describe the measures of maximal entropy for automorphisms with positive entropy.

Foliations on the projective plane with finite group of symmetries

Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine the maximal value that $|\mbox{aut}(\mathcal{F})|$ can take and explicitly exhibit all the foliations attaining this maximal value. Furthermore, we classify the foliations with large but finite automorphism group.

On equivalence problem for 2--nondegenerate CR geometries with simple models

In this article, we solve the equivalence problem for 2--nondegenerate CR geometries that have (at every point) a homogeneous space $G/H$ as a maximally symmetric model for $G$ simple real Lie group of CR automorphisms. This completes the classification of real submanifolds in complex space that are maximally symmetric models with a real simple CR automorphism group. In particular, we construct (local) embeddings of these models into complex space.