Characterizing the unit ball by its projective automorphism group

Characterization of C by its Automorphism Group

Let M be a connected complex manifold of dimension n and let Aut(M) denote the group of holomorphic automorphisms of M . The group Aut(M) is a topological group equipped with the natural compact-open topology. We are interested in the problem of characterizing M by Aut(M). This problem becomes particularly intriguing when Aut(M) is infinite-dimensional. Let, for example, M = C and suppose that ...

THE AUTOMORPHISM GROUP OF FINITE GRAPHS

Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.

On the Unit Ball

Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic selfmap of B and ψ(z) a holomorphic function on B, where B is the unit ball of C n . Let 0 < p, s < +∞,−n− 1 < q < +∞, q+ s > −1 and α ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operatorWψ,φ induced by φ and ψ to be bounded and compact between the space F (p, q, s) and α-Bloch space β.

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

The Automorphism Group of a Lie Group

Introduction. The group A (G) of all continuous and open automorphisms of a locally compact topological group G may be regarded as a topological group, the topology being defined in the usual fashion from the compact and the open subsets of G (see §1). In general, this topological structure of A(G) is somewhat pathological. For instance, if G is the discretely topologized additive group of an i...