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.
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.
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@article{CRMATH_2016__354_2_155_0, author = {Guo, Chang-Yu and Williams, Marshall}, title = {The branch set of a quasiregular mapping between metric manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {155--159}, publisher = {Elsevier}, volume = {354}, number = {2}, year = {2016}, doi = {10.1016/j.crma.2015.10.022}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2015.10.022/} }
TY - JOUR AU - Guo, Chang-Yu AU - Williams, Marshall TI - The branch set of a quasiregular mapping between metric manifolds JO - Comptes Rendus. Mathématique PY - 2016 SP - 155 EP - 159 VL - 354 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.10.022/ DO - 10.1016/j.crma.2015.10.022 LA - en ID - CRMATH_2016__354_2_155_0 ER -
%0 Journal Article %A Guo, Chang-Yu %A Williams, Marshall %T The branch set of a quasiregular mapping between metric manifolds %J Comptes Rendus. Mathématique %D 2016 %P 155-159 %V 354 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.10.022/ %R 10.1016/j.crma.2015.10.022 %G en %F CRMATH_2016__354_2_155_0
Guo, Chang-Yu; Williams, Marshall. The branch set of a quasiregular mapping between metric manifolds. Comptes Rendus. Mathématique, Tome 354 (2016) no. 2, pp. 155-159. doi : 10.1016/j.crma.2015.10.022. http://www.numdam.org/articles/10.1016/j.crma.2015.10.022/
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