Konformikuvaukset ja hyperbolinen metriikka
Authors
Date
2021Tutkielmassa esitellään konformikuvauksia ja niiden merkitystä hyperbolisen geometrian malleissa erityisesti hyperbolisen metriikan suhteen. Tutkielmassa esitellään Poincarén kiekkomallin hyperbolinen metriikka ja tämän avulla määritellään hyperbolinen metriikka myös mielivaltaiselle yhdesti yhtenäiselle alueelle.
Keywords
Metadata
Show full item recordCollections
- Pro gradu -tutkielmat [29740]
License
Related items
Showing items with similar title or keywords.
-
Quasiconformal geometry and removable sets for conformal mappings
Ikonen, Toni; Romney, Matthew (Hebrew University Magnes Press; Springer, 2022)We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain Ω ⊂ ℝ2 that vanishes on a compact set E ⊂ Ω and satisfies mild assumptions. Our main question is to ... -
Two‐dimensional metric spheres from gluing hemispheres
Ikonen, Toni (Wiley-Blackwell, 2022)We study metric spheres (Z,dZ) obtained by gluing two hemispheres of S2 along an orientation-preserving homeomorphism g:S1→S1, where dZ is the canonical distance that is locally isometric to S2 off the seam. We show that ... -
Duality of moduli in regular toroidal metric spaces
Lohvansuu, Atte (Finnish Mathematical Society, 2021)We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala ... -
Yhdesti yhtenäisten tasoalueiden konformisten itsekuvausten ryhmät sup-metriikassa
Syrjälä, Juha (2014) -
On a class of singular measures satisfying a strong annular decay condition
Arroyo, Ángel; Llorente, José G. (American Mathematical Society, 2019)A metric measure space (X, d, t) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that for each x E X and all 0 < r < R. If do., is the distance induced by the co -norm in RN, we ...