Timeline for Pitfalls when generalizing the heat kernel of a Riemannian metric
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2012 at 13:09 | comment | added | Ray Yang | It may not be sufficient for the matrix $(a_{ij})$ to be positive definite. Uniform ellipticity is a pretty standard condition, since if the matrix becomes degenerate in the wrong way quite a few of the desired properties may fail. | |
| Jun 4, 2012 at 14:49 | comment | added | Deane Yang | You can always write your elliptic PDO as the Laplace-Beltrami operator (for the Riemannian metric whose inverse tensor is equal to $a^{ij}$) plus a vector field. So all you need to do is find references that study the heat kernel for an operator like that on a Riemannian manifold. | |
| Jun 4, 2012 at 13:57 | history | asked | Pablo Lessa | CC BY-SA 3.0 |