Journal:
:Bulletin Of The Brazilian Mathematical Society, New Series2023
Given a Galois extension $$R^{\beta } \subset R$$ , where $$\beta $$ is an action of finite groupoid on noncommutative ring, we present some conditions to the map be injective.
Given a smooth compact Riemannian surface, we prove that if a suitable convexity assumption on the tangent focal cut loci is satisfied, then all injectivity domains are semiconvex.
