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The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite DAngelo type. The method of proof is new so that it simplifies the previous proof of earlier semicontinuity theorems on bounded strongly pseudoconvex daomains by Greene and Krantz in the early 1980s.
We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and $Theta$-reductivity of the moduli of K-semistable log Fano pairs. A
We make a connection between the structure of the bidisc and a distinguished subgroup of its automorphism group. The automorphism group of the bidisc, as we know, is of dimension six and acts transitively. We observe that it contains a subgroup that
We study fixed point properties of the automorphism group of the universal Coxeter group Aut$(W_n)$. In particular, we prove that whenever Aut$(W_n)$ acts by isometries on complete $d$-dimensional CAT$(0)$ space with $d<lfloorfrac{n}{2}rfloor$, then
In this note, we consider the sufficient coefficient condition for some harmonic mappings in the unit disk which can be extended to the whole complex plane. As an application of this result, we will prove that a harmonic strongly starlike mapping has
The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by Lie homomorp