Highly regular Peano surjections
Event details
| Date | 17.06.2010 |
| Hour | 13:15 |
| Speaker | Jeremy Tyson (Urbana-Champaign and UniBern) |
| Location |
MA-12
|
| Category | Conferences - Seminars |
We study space filling mappings of high regularity. According to the
classical results of Peano, Hahn and Mazurkiewicz, every compact,
connected and locally connected metric space is the continuous image of
the closed unit interval. We prove that every compact geodesic metric
space is the image of the closed unit ball in $R^n$ for each $nge 2$ by a
continuous mapping in the Sobolev class $W^{1,n}$. Here we use the notion
of metric space-valued Sobolev mapping introduced by Ambrosio (1990) and
Reshetnyak (1997). We also study the space filling problem for Lipschitz
and Holder mappings. As an application, we show that the first Heisenberg
group, equipped with its Carnot-Caratheodory metric, is the Lipschitz
image of $R^5$.
Links
Practical information
- General public
- Free
Contact
- Marc Troyanov