What question did this study set out to answer?

The aim is to generalize the univalence on the boundary theorem from complex analysis using topological principles.

January 23, 2026Axioms0 citationsOpen Access

On the Theorem of Univalence on the Boundary

Key Points

The aim is to generalize the univalence on the boundary theorem from complex analysis using topological principles.
Develop several generalizations of the known univalence theorem
Utilize topological results for formulations
Apply findings to Sobolev mappings
Established new univalence conditions applicable to Sobolev mappings
Linked topological aspects to complex analysis theorems

Abstract

We give several generalizations of a known theorem from complex analysis, namely the univalence on the boundary theorem. Starting from a purely topological result (Theorems 1 and 11), we obtain univalence conditions for Sobolev mappings.

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