Mathematics – Dynamical Systems
Scientific paper
1991-11-26
Mathematics
Dynamical Systems
Scientific paper
Let $K$ be a compact subset of $\bar{\bold C} ={\bold R}^2$ and let $K^c$ denote its complement. We say $K\in HR$, $K$ is holomorphically removable, if whenever $F:\bar{\bold C} \to\bar{\bold C}$ is a homeomorphism and $F$ is holomorphic off $K$, then $F$ is a M\"obius transformation. By composing with a M\"obius transform, we may assume $F(\infty )=\infty$. The contribution of this paper is to show that a large class of sets are $HR$. Our motivation for these results is that these sets occur naturally (e.g. as certain Julia sets) in dynamical systems, and the property of being $HR$ plays an important role in the Douady-Hubbard description of their structure.
No associations
LandOfFree
On removable sets for Sobolev spaces in the plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On removable sets for Sobolev spaces in the plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On removable sets for Sobolev spaces in the plane will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-675401