Timeline for An unpublished result of H. Hamm
Current License: CC BY-SA 4.0
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| Jun 15, 2020 at 12:26 | comment | added | user2520938 | @ViditNanda Thanks for your comment. In the article you mention it seems though that the singular locus of $f^{-1}(0)$ has to be compact. Now I'm really looking for a general result, so I do not think that this article really contains what I'm looking for. I will take a look at citing literature though, thanks. | |
| Jun 15, 2020 at 11:48 | comment | added | Vidit Nanda | Note that sets like $\{|f(x)| < p\}$ are equivalent to $\{|f(x)|^2 < p^2\}$ and the norm-squared function is much friendlier to work with (eg it is smooth). I don't know if your desired result has appeared anywhere, but I think a good starting point is Durfee's paper (jstor.org/stable/1999065). This does what you want globally, ie., without the $\{|x|<R\}$ part; to make the equivalence local, you have to show that the gradient vector field of $-|f|^2$ points inwards along the boundary $\{|x|=R\} - \{f=0\}$. | |
| Jun 15, 2020 at 10:57 | history | edited | user2520938 | CC BY-SA 4.0 |
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| Jun 15, 2020 at 10:44 | history | asked | user2520938 | CC BY-SA 4.0 |