Javad Mashreghi (Laval University)

will speak on

A New Link Between Convexity and Double-Layer Potentials

Time: 3:00PM
Date: Tue 11th November 2025
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: Let $\Omega$ be a simply connected domain in the complex plane, and let $\phi : \mathbb{D} \to \Omega$ be a conformal mapping from the open unit disk $\mathbb{D}$ onto $\Omega$. It is well known that $\Omega$ is convex if and only if
$$
\Re \left( \frac{z \phi''(z)}{\phi'(z)} \right) \ge -1, \quad z \in \mathbb{D}.
$$
We show that this relation is, in fact, inherited by a single Blaschke factor, and that when considering the family of all finite Blaschke products, entirely new intrinsic properties of $\phi$ are revealed.

This is an ongoing research with T. Ransford, Oliver Roth and Annika Moucha.

https://ucd-ie.zoom.us/j/63440321261

(This talk is part of the Analysis series.)

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