Mappings of Finite Distortion : Compactness of the Branch Set
Kauranen, A., Luisto, R., & Tengvall, V. (2021). Mappings of Finite Distortion : Compactness of the Branch Set. Journal d'Analyse Mathematique, 143(1), 207-229. https://doi.org/10.1007/s11854-021-0153-8
Julkaistu sarjassa
Journal d'Analyse MathematiquePäivämäärä
2021Tekijänoikeudet
© 2021 The Hebrew University of Jerusalem
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to an (n − 2)-dimensional torus and distortion arbitrarily close to the asymptotic bound.
Julkaisija
Hebrew University Magnes Press; SpringerISSN Hae Julkaisufoorumista
0021-7670Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/72827016
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Tutkijatohtori, SA; Akatemiahanke, SALisätietoja rahoituksesta
A. K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “María de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0445) and MTM-2016-77635-P (MICINN, Spain) and Academy of Finland project 322441. R. L. was supported by the Finnish Academy of Science and Letters. V. T. was supported by the Academy of Finland Projects 277923 and 308759.![showless](/themes/JYX2//images/showless.png)
![showmore](/themes/JYX2//images/showmore.png)
Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Mappings of Finite Distortion : Compactness of the Branch Set
Kauranen, Aapo; Luisto, Rami; Tengvall, Ville (2018)We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing ... -
Mappings of finite distortion : size of the branch set
Guo, Chang-Yu; Hencl, Stanislav; Tengvall, Ville (De Gruyter, 2020)We study the branch set of a mapping between subsets of Rn, i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have ... -
Open and discrete maps with piecewise linear branch set images are piecewise linear maps
Luisto, Rami; Prywes, Eden (Wiley-Blackwell, 2021)The image of the branch set of a piecewise linear (PL)‐branched cover between PL 𝑛n‐manifolds is a simplicial (𝑛−2)(n−2)‐complex. We demonstrate that the reverse implication also holds: an open and discrete map ... -
Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds
Nobili, Francesco; Violo, Ivan Yuri (Springer Science and Business Media LLC, 2022)We prove that if M is a closed n-dimensional Riemannian manifold, n \ge 3, with \mathrm{Ric}\ge n-1 and for which the optimal constant in the critical Sobolev inequality equals the one of the n-dimensional sphere \mathbb ... -
Parakompaktius
Varis, Valtteri (2023)Tämä tutkielma on katsaus topologiaan keskittyen etenkin parakompaktiuteen ja avaruuksien metristyvyyteen. Tutkielmassa esitellään topologian perusteet avoimista joukoista alkaen ja tämän jälkeen käydään läpi tarvittavia ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.