Timeline for Measure of the boundary of Alexandrov space
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2021 at 1:28 | comment | added | Adterram | @AntonPetrunin "Regular points of extremal subsets in Alexandrov spaces" by Fujioka is a reference. Not sure if there are any earlier reference. | |
| Jun 8, 2021 at 3:38 | comment | added | Anton Petrunin | @Totoro any extremal subset have a regular point; if needed I will find a reference. | |
| Jun 8, 2021 at 2:59 | comment | added | Totoro | Why does $\partial X$ contain a regular point? | |
| Jun 8, 2021 at 2:35 | comment | added | Anton Petrunin | @Totoro A point $p$ is a regular point of subset S if the tangent space $T_pS$ is Euclidean. | |
| Jun 8, 2021 at 2:25 | comment | added | Totoro | May I ask what is the definition of a regular point in $T_p(\partial X)$? As $\partial X$ may not be an Alexandrov space, the definition is unclear to me. Anyway, one can use the same method and prove by induction that any $m$-dimensional extremal set contains a "cube" which is the image of $I^m$ such that the opposite faces of the cube have positive distance. | |
| Jun 7, 2021 at 23:04 | comment | added | Anton Petrunin | @Totoro, it is fixed now, thank you. | |
| Jun 7, 2021 at 23:04 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
positive measure -- thanks to Totoro
|
| Jun 7, 2021 at 10:32 | comment | added | Totoro | It seems to me that this argument only shows $dim_H \partial X \le n-1$. How can one prove $H_{n-1}(\partial X)>0$? | |
| Nov 18, 2019 at 7:42 | vote | accept | asv | ||
| Nov 18, 2019 at 1:50 | history | answered | Anton Petrunin | CC BY-SA 4.0 |