Timeline for Can a 2-sphere be squashed flat?
Current License: CC BY-SA 4.0
7 events
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| Aug 29 at 19:05 | comment | added | tomasz | I think this should probably follow also from the remarks in the lecture notes linked in the other answer. Specifically, they provide an argument that a length-preserving function cannot be injective on any open set, which for $C^1$ functions implies that the differential is singular everywhere, which should contradict preserving lengths (but my differential geometry is a bit rusty, so don't quote me on that). | |
| Aug 27 at 20:35 | comment | added | Denis T | By the way, is it true that if a Finsler sphere was not already conformally (Alexandrov) flat, then it cannot be $C^1$ squashed? | |
| Aug 27 at 18:40 | history | edited | Amir Sagiv | CC BY-SA 4.0 |
Extremely minor tex edits
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| Aug 27 at 18:24 | comment | added | Graham Smith | That's an interesting complement. Thankyou very much! | |
| Aug 27 at 17:28 | history | edited | Guido De Philippis | CC BY-SA 4.0 |
Updated according to the new references.
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| Aug 27 at 16:34 | history | edited | Guido De Philippis | CC BY-SA 4.0 |
added 495 characters in body
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| Aug 27 at 16:22 | history | answered | Guido De Philippis | CC BY-SA 4.0 |