This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature≥-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eig...This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature≥-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eigenvalue of M. Then there exists a constant Cm dependent only on m such展开更多
Let M be a compact Riemann manifold with the Ricci curvature ≥ - R（R = const. 】0）. Denote by d the diameter of M. Then the first eigenvalue λ<sub>1</sub> of M satisfies λ<sub>1</sub>≥（...Let M be a compact Riemann manifold with the Ricci curvature ≥ - R（R = const. 】0）. Denote by d the diameter of M. Then the first eigenvalue λ<sub>1</sub> of M satisfies λ<sub>1</sub>≥（π<sup>2</sup>/d<sup>2</sup>）-0.52 R. Moreover if R≤（5π<sup>2</sup>）/（3d<sup>2</sup>）, then λ<sub>1</sub>≥（π<sup>2</sup>/d<sup>2</sup>）-（R/2）.展开更多
This paper deals with a class of parabolic Monge-Ampère equation on Riemannian manifolds. The existence and uniqueness of the solution to the first initial-boundary value problem for the equation are established.
基金Partially supported by the National Natural Science Foundation of China
文摘This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature≥-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eigenvalue of M. Then there exists a constant Cm dependent only on m such
文摘Let M be a compact Riemann manifold with the Ricci curvature ≥ - R（R = const. 】0）. Denote by d the diameter of M. Then the first eigenvalue λ<sub>1</sub> of M satisfies λ<sub>1</sub>≥（π<sup>2</sup>/d<sup>2</sup>）-0.52 R. Moreover if R≤（5π<sup>2</sup>）/（3d<sup>2</sup>）, then λ<sub>1</sub>≥（π<sup>2</sup>/d<sup>2</sup>）-（R/2）.
文摘This paper deals with a class of parabolic Monge-Ampère equation on Riemannian manifolds. The existence and uniqueness of the solution to the first initial-boundary value problem for the equation are established.
