Volume 3, Issue 3
The Heat Kernel on Constant Negative Curvature Space Form

Li Jiayu

DOI:

J. Part. Diff. Eq.,3(1990),pp.54-62

Published online: 1990-03

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  • Abstract

Let M be a n-dimensional simply connected, complete Riemannian manifold with constant negative curvature. The heat kernel on M is denoted by H^M_t(x, y) = H^M_t(r(x, y)), where r(x, y) = dist(x, y). We have the explicit formula of H^M_t(x, y) for n=2, 3, and the induction formula of H^M_t(x, y) for n ≥ 4^{[-1]}. But the explicit formula is very complicated for n ≥ 4. ln this paper we give some simple and useful global estimates of H^M_t(x, y), and apply these estimates to the problem of eigenvalue.

  • Keywords

Constant negative curvature space form heat kernel eigenvalue

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@Article{JPDE-3-54, author = {Li Jiayu}, title = {The Heat Kernel on Constant Negative Curvature Space Form}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {3}, pages = {54--62}, abstract = { Let M be a n-dimensional simply connected, complete Riemannian manifold with constant negative curvature. The heat kernel on M is denoted by H^M_t(x, y) = H^M_t(r(x, y)), where r(x, y) = dist(x, y). We have the explicit formula of H^M_t(x, y) for n=2, 3, and the induction formula of H^M_t(x, y) for n ≥ 4^{[-1]}. But the explicit formula is very complicated for n ≥ 4. ln this paper we give some simple and useful global estimates of H^M_t(x, y), and apply these estimates to the problem of eigenvalue.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5806.html} }
TY - JOUR T1 - The Heat Kernel on Constant Negative Curvature Space Form AU - Li Jiayu JO - Journal of Partial Differential Equations VL - 3 SP - 54 EP - 62 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5806.html KW - Constant negative curvature space form KW - heat kernel KW - eigenvalue AB - Let M be a n-dimensional simply connected, complete Riemannian manifold with constant negative curvature. The heat kernel on M is denoted by H^M_t(x, y) = H^M_t(r(x, y)), where r(x, y) = dist(x, y). We have the explicit formula of H^M_t(x, y) for n=2, 3, and the induction formula of H^M_t(x, y) for n ≥ 4^{[-1]}. But the explicit formula is very complicated for n ≥ 4. ln this paper we give some simple and useful global estimates of H^M_t(x, y), and apply these estimates to the problem of eigenvalue.
Li Jiayu. (1970). The Heat Kernel on Constant Negative Curvature Space Form. Journal of Partial Differential Equations. 3 (3). 54-62. doi:
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