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 &#8805 4^{[-1]}. But the explicit formula is very complicated for n &#8805 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.