完备流形上带位势的热核估计

Estimates of Heat Kernel with Potential on Complete Manifold

在完备非紧流形上获得了关于带位势热方程正解的梯度估计 ;接着 ,利用测地线的技巧获得了 Harnack不等式 ;进一步 ,建立了两个积分不等式 ,综合 Harnack不等式获得了热核的上下界 ;最后 ,利用函数的结果来控制 p-形式的热核 .

First the author gets a gradient estimate of the heat equation's positive solution with potential on a complete manifold which is not compact; secondly, the author uses the technique of geodesic to get Harnack inequalities;moreover, the author eatablishes two integral inequalities; together with Harnack inequalities, the author gets the upper and lower bounds of heat kernels; at last, the author uses function's result to dominant heat kernel of \%p\% forms.