S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length o...S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length of the second fundamental form as a function on this set. Is the image of this function a discrete set of positive numbers?展开更多
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
<正> The estimations of decreasing coefficients on K-dilatation harmonic maps, which were given by [1—3], are not precise. In fact, using the authors’ methods, we can readily obtain more precise estimations. L...<正> The estimations of decreasing coefficients on K-dilatation harmonic maps, which were given by [1—3], are not precise. In fact, using the authors’ methods, we can readily obtain more precise estimations. Let M be an m-dimensional Riemannian manifold, N be an n-dimensional Rieman nian manifold, {θ~i} and {ω~α} be normally orthornal coframes on M and N respec-展开更多
Ⅰ. INTRODUCTION Let M(·) be a convex increasing function over [0, +∞),f(·) be a non-negative function of bounded variation over [0, a] and M(0)=f(0)=0. In this paper, we shall give the
文摘S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length of the second fundamental form as a function on this set. Is the image of this function a discrete set of positive numbers?
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<正> The estimations of decreasing coefficients on K-dilatation harmonic maps, which were given by [1—3], are not precise. In fact, using the authors’ methods, we can readily obtain more precise estimations. Let M be an m-dimensional Riemannian manifold, N be an n-dimensional Rieman nian manifold, {θ~i} and {ω~α} be normally orthornal coframes on M and N respec-
文摘Ⅰ. INTRODUCTION Let M(·) be a convex increasing function over [0, +∞),f(·) be a non-negative function of bounded variation over [0, a] and M(0)=f(0)=0. In this paper, we shall give the
