On Weak 1-Semiconvexity of Open Sets in Euclidean Spaces

Explore the concept of weakly 1-semiconvex sets in n-dimensional real Euclidean spaces through this 19-minute lecture from the HyperComplex Seminar. Delve into the generalization of linearly accessible domains in the plane and their connection to univalent functions theory. Examine how weakly 1-semiconvex sets can be disconnected and under certain conditions, how this property necessarily implies disconnectedness in the plane. Learn about the origins of this newish theory, coined by Yurii Zelinskii, and understand the formal definition of weakly 1-semiconvex open subsets in Rn. Investigate the concept of 1-nonsemiconvexity points and their corresponding sets, gaining insights into this advanced mathematical topic.