In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison...In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison theorem for the weighted heat kernel. In the second part, we establish two gap results for the Ricci curvature and the scalar curvature, based on which some rigid properties can be derived.展开更多
基金supported by Natural Science Foundation of Jiangsu Province (Grant No. BK20141235)
文摘In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison theorem for the weighted heat kernel. In the second part, we establish two gap results for the Ricci curvature and the scalar curvature, based on which some rigid properties can be derived.
