Timeline for Sobolev embedding in complete manifold
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2019 at 11:10 | comment | added | Adrián González Pérez | In general, Sobolev inequalities on manifolds can be to much to ask. That inequality would imply that the volume of the balls grow faster that $r^n$. In particular it would be false in spaces like $\mathbb{R}^n \# \mathbb{R}^n$. Local or scale-invariant versions of the Sobolev inequalities are much more stable. I suggest you have a look at Saloff-Coste "Aspect of Sobolev type inequalities". There is also a nice survey "Sobolev inequalities in familiar and unfamiliar settings" of the same author in a book edited by Maz'ya. | |
| Feb 19, 2019 at 13:20 | comment | added | Ben McKay | I think this is Theorem 3.14, p. 31 of Hebey, Sobolev Spaces on Riemannian Manifolds, with the hypothesis that (a) Ricci is bounded below and (b) volumes of unit balls are bounded below by a positive constant. But the precise statement is a little tricky to dig out of the book, so I am not sure. | |
| Feb 19, 2019 at 11:53 | history | edited | DLIN | CC BY-SA 4.0 |
added 97 characters in body
|
| Feb 19, 2019 at 11:01 | history | edited | YCor |
edited tags
|
|
| Feb 19, 2019 at 10:38 | history | edited | DLIN |
edited tags
|
|
| Feb 19, 2019 at 8:32 | history | asked | DLIN | CC BY-SA 4.0 |