We establish two-point distortion theorems for sense-preserving planar harmonic mappings $$f=h+\overline{g}$$ in the unit disk $${\mathbb D}$$ which satisfy versions of univalence criteria due to Becker and Nehari. In addition, we also find cases when h is a normalized convex function and, more generally, $$h({\mathbb D})$$ c-linearly connected domain.

We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both fibrant and non-fibrant types. The fibrant fragment includes Voevodsky’s univalence axiom and a circle type, while the non-fibrant fragment includes exact (strict) equality types satisfying equality reflection. Our type theory is defined by a semantics in cu...

it is known that the condition $mathfrak {re} left{zf'(z)/f(z)right}>0$, $|z|