Local homeomorphisms satisfying generalized modular inequalities

Abstract

We study the geometric properties of the local homeomorphisms satisfying some generalized modular inequalities. We establish in Theorem 1 that a local homeomorphism f : D ⊂ R n → R n satisfying condition (N ) and having local AC L q inverses, with q > 1, satisfy important modular inequalities. We generalize in this class of mappings known theorems from the theory of quasiregular mappings like Zoric's theorem and the estimate of the radius of injectivity.

On boundary behavior of spatial mappings

“…It is well-known that the concept of moduli with weights essentially due to Andreian Cazacu, see, e.g., [1]- [3], see also recent works [6]- [8] of her learner. At the present paper we give new modulus estimates for space mappings that essentially improve the corresponding estimates first obtained in the paper [23].…”