Timeline for Metric measure spaces: in what sense is analysis on these spaces "non-smooth"
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2020 at 16:55 | comment | added | Behnam Esmayli | From what I gather throughout the answers and comments, here "non-smooth" has been used just because it was something new! Just like everything new in math has been called irratonal, irregular, fractal (broken),... I believe "analysis on metric spaces" is a much better terminology. | |
| Mar 5, 2020 at 18:11 | history | edited | YCor | CC BY-SA 4.0 |
removed tag, removed capitals, specified a bit the title
|
| Mar 5, 2020 at 18:05 | comment | added | Piotr Hajlasz | @Wojowu Actually in many situation there are "differentiable" mappings between metric spaces. In particular Cheeger proved existence of a measurable differentiable structure on spaces supporting Poincare inequalities. | |
| Mar 5, 2020 at 15:13 | answer | added | Piotr Hajlasz | timeline score: 7 | |
| Jan 29, 2019 at 15:29 | vote | accept | yoshi | ||
| Jan 28, 2019 at 19:59 | comment | added | Dirk | I would compare to the analysis on the "smoothest" spaces, i.e. real vector spaces with an inner product. | |
| Jan 28, 2019 at 18:25 | answer | added | user135139 | timeline score: 11 | |
| Jan 28, 2019 at 14:55 | comment | added | Piotr Hajlasz | Another example is analysis on Cantor sets. No smooth structures. Since you are at Stony Brook you should talk to Raanan Schul or Silvia Ghinassi. They would provide you many interesting examples. | |
| Jan 28, 2019 at 14:39 | comment | added | David Hughes | One example that comes to mind is the class of Alexandrov spaces, which can be thought of as limits of smooth manifolds. For example the distance function is never smooth on a compact smooth manifold, I think. | |
| Jan 28, 2019 at 14:28 | comment | added | Wojowu | It simply has to do with the fact there is no notion of a smooth or differentiable function between metric measure spaces. | |
| Jan 28, 2019 at 14:26 | history | asked | yoshi | CC BY-SA 4.0 |