A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Pullback of a quasiconformal map between arbitrary metric measure spaces (2024)
Ikonen, T., Lučić, D., & Pasqualetto, E. (2024). Pullback of a quasiconformal map between arbitrary metric measure spaces. Illinois Journal of Mathematics, Early online. https://doi.org/10.1215/00192082-11081290
JYU-tekijät tai -toimittajat
Julkaisun tiedot
Julkaisun kaikki tekijät tai toimittajat: Ikonen, Toni; Lučić, Danka; Pasqualetto, Enrico
Lehti tai sarja: Illinois Journal of Mathematics
ISSN: 0019-2082
eISSN: 1945-6581
Julkaisuvuosi: 2024
Ilmestymispäivä: 01.01.2024
Volyymi: Early online
Kustantaja: Duke University Press
Julkaisumaa: Yhdysvallat (USA)
Julkaisun kieli: englanti
DOI: https://doi.org/10.1215/00192082-11081290
Julkaisun avoin saatavuus: Ei avoin
Julkaisukanavan avoin saatavuus:
Rinnakkaistallenteen verkko-osoite (pre-print): https://arxiv.org/abs/2112.07795
Tiivistelmä
We prove that every (geometrically) quasiconformal homeomorphism between metric measure spaces induces an isomorphism between the cotangent modules constructed by Gigli. We obtain this by first showing that every continuous mapping φ with bounded outer dilatation induces a pullback map φ∗ between the cotangent modules of Gigli, and then proving the functorial nature of the resulting pullback operator. Such pullback is consistent with the differential for metric-valued locally Sobolev maps introduced by Gigli–Pasqualetto–Soultanis. Using the consistency between Gigli’s and Cheeger’s cotangent modules for PI spaces, we prove that quasiconformal homeomorphisms between PI spaces preserve the dimension of Cheeger charts, thereby generalizing earlier work by Heinonen–Koskela–Shanmugalingam–Tyson. Finally, we show that if φ is a given homeomorphism with bounded outer dilatation, then φ−1 has bounded outer dilatation if and only if φ∗ is invertible and φ−1 is Sobolev. In contrast to the setting of Euclidean spaces, Carnot groups, or more generally, Ahlfors regular PI spaces, the Sobolev regularity of φ−1 needs to be assumed separately.
YSO-asiasanat: differentiaaligeometria; funktionaalianalyysi
Liittyvät organisaatiot
OKM-raportointi: Kyllä
Alustava JUFO-taso: 1
