Timeline for Asymptotic of the heat kernel
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Oct 15, 2013 at 18:20 | answer | added | Matthias Ludewig | timeline score: 1 | |
| Oct 8, 2013 at 18:49 | comment | added | BewSMA | $Q_k(t,x,y)$ is quite complicated and it can be thought as a smooth function on $[0,\infty)\times M\times M$ with the estimate $|Q_k|\leq C t^{k-n/2}$ on $[0,T]\times M \times M$ and $C=C(T,M)$. The integer $k$ is chosen large with $k-n/2 >2$. | |
| Oct 8, 2013 at 18:37 | comment | added | BewSMA | The following is the link to his book: math.bu.edu/people/sr/articles/book.pdf For a short answer, $H_k = \eta S_k$ where $\eta$ is the cut-off function in the ball of injectivity radius(assuming positive) and $S_k$ is given by $$ S_k = (4\pi t)^{-n/2}e^{-r^2(x,y)/4t}(u_0(x,y)+\cdots +t^k u_k(x,y)) $$ where $u_i$'s satisfy certain recurrence relation and they can be thought as smooth function on $M\times M$. | |
| Oct 8, 2013 at 18:34 | comment | added | Nate Eldredge | For those without the book in front of them, what are $H_k$ and $Q_k$? | |
| Oct 8, 2013 at 17:27 | history | asked | BewSMA | CC BY-SA 3.0 |