Injectivity Theorem Research Articles

Schwarzian derivative in Kähler manifolds (II)

Two injectivity theorems are proved which are for objective manifoldN = ℂℙn andN =B n (unit ball), both equipped with canonical metric. Thus, the injectivity theorems are established in three cases of objective manifolds, i.e. with different holomorphic sectional curvatures - 1, 0 and 1 respectively.

Stability property of Möbius mappings

Let F F be an arbitrary class of continuous mappings acting and ranging on domains in R n {{\mathbf {R}}^n} which is invariant under similarity transformations of R n {{\mathbf {R}}^n} and the restriction of a map to any subdomain. The class Möb of Möbius mappings acting in R n {{\mathbf {R}}^n} is of particular interest. Assume that the class F F is " c c -uniformly close" to Möb. Then we show that any map in F F is either constant or a local quasiconformal homeomorphism. As a corollary we obtain a distinctly elementary proof of the Local Injectivity Theorem for quasiregular mappings.

Injectivity theorems in plane and space

Injectivity theorems in plane and space