完备非紧流形上Schrdinger算子的加权热容度

Weighted Heat Content of a Schrdinger Operator on Complete Noncompact Manifolds

在几何分析中,加权Hodge-Laplacian算子非常重要,在酉等价的意义下,它表现为初始度量的Schrdinger算子.另外,完备非紧流形上热容度问题是几何分析中的一个有趣的问题,在这方面亦有不少研究结果.文章首先给出了相应于初值的Schrdinger算子的加权热容度的定义;进一步,在权函数满足一定条件下,利用热核的性质以及Hlder不等式,得到加权热容度的上界估计.

In geometric analysis, the weighted Hodge-Laplacian operator is important and expresses as a Schr6dinger operator of the initial metric in the unitarily equivalent sense. On the other hand, the heat content question on a complete noncompact manifold is an interesting question in geometric analysis, there are many results in this direction. This paper firstly attempted to define the weighted heat content of the Schrodinger operator associated with a given initial value. Furthermore, by using the properties of the heat kernel and the Ho1der inequality, an upper bound estimate of the heat content under suitable conditions of the weighted function was established.