# Kostiantyn Drach

## "Geometry of λ-convex domains"

 Date: Tue, December 6, 2016 Time: 14:15 Place: Research I Seminar Room

Abstract: In the talk I will introduce the notion of $$\lambda$$-convexity - a natural generalisation of usual convexity - and discuss its connection to the celebrated Blaschke Rolling Theorem. Moreover, I will present some extreme properties of $$\lambda$$-convex domains. In particular, we will see how to reverse the classical isoperimetric problem for such domains. Depending on time availability, ideas and methods of proofs, as well as some open questions, will be outlined with lesser or greater details during the talk. Only modest background in Riemannian geometry is assumed.