Timeline for Have heat kernels for generalized Laplacians on non-compact manifolds been constructed?
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| Nov 11, 2017 at 15:55 | comment | added | Bombyx mori | The construction of heat kernel for manifold with smooth boundary is done in Ray-Singer's [first paper][1] using the parametrix method, where the non-compactness is dealt with using layered potentials. Depending on the shape of your boundary, in general you may need to do multiple rounds of blow ups. [1]: ms.uky.edu/~hislop/papers/ray-singer1.pdf | |
| Feb 19, 2015 at 19:05 | comment | added | Alex M. | If I'm reading Chavel correctly, completeness too is not used. Fundamental solutions to the heat equation are constructed for general manifolds. Both completeness and the lower-boundedness of the Ricci curvature are needed only for uniqueness. (Uniquness is proved in Theorem 3 on page 183, following Dodziuk; existence is proved in Lemma 3 and Theorem 4 on pages 187-191). | |
| Feb 13, 2015 at 1:24 | comment | added | Vesselin Dimitrov | Have you looked at Ma and Marinescu, Holomorphic Morse inequalities and Bergman kernels (Progress in Math, 2007), particularly Appendix D? | |
| Jan 29, 2015 at 11:17 | history | edited | Giovanni De Gaetano | CC BY-SA 3.0 |
Restyling of the question
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| Jan 28, 2015 at 14:56 | history | asked | Giovanni De Gaetano | CC BY-SA 3.0 |