Workshop on the h-principle and beyond

Regularity of the limit set of embedded Poincaré Disks

Abstract: Let f be an embedding of a non compact manifold into an Euclidean space and p_n be a divergent sequence of points of M. If the image points f(p_n) converge, the limit is called a limit point of f. In this talk, we will build an embedding f of a closed disk into a 3-Euclidean ball whose restriction to the interior is a C^1 embedding of the Poincaré disk and which is, on the closed disk, \beta-Hölder for any 0<\beta<1. In particular, this embedding of the Poincaré disk has a closed embedded curve of Hausdorff dimension one as limit set. 

Date & Time

November 04, 2021 | 9:00am – 10:00am


Simonyi 101 and Remote Access


Vincent Borelli

Speaker Affiliation

University of Lyon