Comptes Rendus
no. 2
Complex analysis/Topology
The branch set of a quasiregular mapping between metric manifolds

Presented by: the Editorial Board

Chang-Yu Guo1; Marshall Williams2
1 Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland
2 Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA
Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 155-159.

In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fässler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.

Dans cette note, nous annonçons de nouveaux résultats quant à la porosité dénombrable quantitative de l'ensemble des branchements d'une application quasi régulière dans un cadre très général d'espaces métriques. Comme applications de nos résultats, nous répondons à une conjecture récente de Fässler et al., à un problème ouvert de Heinonen–Rickman et à une question ouverte de Heinonen–Semmes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.10.022

Chang-Yu Guo 1; Marshall Williams 2

1 Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 Jyväskylä, Finland
2 Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA 
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Chang-Yu Guo; Marshall Williams. The branch set of a quasiregular mapping between metric manifolds. Comptes Rendus. Mathématique, Volume 354 (2016) no. 2, pp. 155-159. doi : 10.1016/j.crma.2015.10.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.022/

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