Timeline for Are Hölder manifolds a thing?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 15 at 16:02 | comment | added | Sidharth Ghoshal | Did you get a chance to look further into this? I wonder if there exist "exotic holder spheres" or similarly "exotic holder <insert manifold here>"? | |
| Jan 5, 2020 at 14:53 | answer | added | Vitali Kapovitch | timeline score: 11 | |
| Dec 22, 2019 at 12:26 | comment | added | Pietro Majer | For instance, Lipschitz perturbations of a hyperbolic operator are Hölder-conjugate, (and in general not Lipschitz-conjugate, even in smooth cases), by the Hartman-Grobman thm. | |
| Dec 22, 2019 at 10:53 | comment | added | ThiKu | Hölder structures play a role in the study of maps between hyperbolic spaces because the boundary of a hyperbolic space has a canonical Hölder structure, albeit not a canonical $C^\infty$-structure: any two visual metrics on the boundary of a hyperbolic space are Hölder-equivalent. Quasi-isometries between spaces induce bi-Hölder maps between the boundaries. See I.Kapovich-N.Benakli, Section 3. | |
| Dec 22, 2019 at 10:26 | comment | added | Nicola Ciccoli | Not quite what you're asking for but let me comment that $C^{1+\alpha}$ manifolds were considered in the context of topological dynamics by Sullivan in the 80ies. math.stonybrook.edu/~dennis/publications/PDF/DS-pub-0079.pdf | |
| Dec 22, 2019 at 9:15 | history | asked | shuhalo | CC BY-SA 4.0 |