Timeline for Log of heat kernel for positive time
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2016 at 8:24 | comment | added | Alex M. | The article linked by @littlelittlelittle has moved to msc.tsinghua.edu.cn/~gxu/public/JDG.pdf. Nevertheless, the reader is warned that it doesn't address the question asked by the OP. | |
| Oct 15, 2014 at 18:31 | comment | added | Justin | @Joonas, I'll admit my question is a bit vague. Basically, a few algorithms in geometry processing use the heat kernel and justify it via this Varadhan paper. This of course is a perfectly acceptable argument, but I'm hoping to understand what happens as you deviate from the $t\rightarrow0$ case. | |
| Oct 14, 2014 at 14:32 | comment | added | littlelittlelittle | there is a recent paper on the long time behavior of heat kernel, see msc.tsinghua.edu.cn/~gxu/Public/large%20time%20behavior.pdf | |
| Oct 12, 2014 at 7:29 | comment | added | Joonas Ilmavirta | If your manifold is closed, then the heat equation drives a function towards its average and so $p(t,x,y)\to V^{-1}$ as $t\to\infty$, where $V$ is the volume of the manifold. If you want to say something about $-2t\log p$ for any fixed $t>0$, your statement should remain true in the limit $t\to\infty$ when $p$ becomes independent of $x$ and $y$. Also, if $t$ is fixed and $x$ is very close to $y$, we have $p(x,t,y)>1$ and your "distance" is negative. Can you be more specific about what you would like to have? | |
| Oct 12, 2014 at 7:06 | history | asked | Justin | CC BY-SA 3.0 |