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 that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.
LetM be a compact Riemann manifold with the Ricci curvature ? - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - 0.52R$ ...LetM be a compact Riemann manifold with the Ricci curvature ? - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - 0.52R$ . Moreover if $R \leqslant \frac{{5\pi ^2 }}{{3d^2 }}$ , then $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - \frac{R}{2}$展开更多
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 that
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.
文摘LetM be a compact Riemann manifold with the Ricci curvature ? - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - 0.52R$ . Moreover if $R \leqslant \frac{{5\pi ^2 }}{{3d^2 }}$ , then $\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - \frac{R}{2}$
