This paper establishes a new Laplacian comparison theorem which is specially useful tothe mathelds of nonpositive curvature. It leads naturally to the corresponding heat kernelcomparison and eigenvalue comparison theo...This paper establishes a new Laplacian comparison theorem which is specially useful tothe mathelds of nonpositive curvature. It leads naturally to the corresponding heat kernelcomparison and eigenvalue comparison theorems. Furthermore, a lower estimate of L2-spectrumof an n-dimensional non-compact complete Cartan-Hadamard manifold is given by (n-1)k/4,provided its mRicci curvature -(n -1)k (k= const. 0).展开更多
文摘This paper establishes a new Laplacian comparison theorem which is specially useful tothe mathelds of nonpositive curvature. It leads naturally to the corresponding heat kernelcomparison and eigenvalue comparison theorems. Furthermore, a lower estimate of L2-spectrumof an n-dimensional non-compact complete Cartan-Hadamard manifold is given by (n-1)k/4,provided its mRicci curvature -(n -1)k (k= const. 0).
