In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negativ...In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius, which improves some results in [4].展开更多
15岁的徐安庐求学经历颇为传奇。两岁时以乐高组合玩具组成与自己同高的机器人,5岁时已能解简单的代数题目,6岁智商超出量表能测出的范围,8岁起开始在家自学,11岁赢得华盛顿州高中组科展大奖,成为历届年纪最小的大奖得主,并代表华盛顿...15岁的徐安庐求学经历颇为传奇。两岁时以乐高组合玩具组成与自己同高的机器人,5岁时已能解简单的代数题目,6岁智商超出量表能测出的范围,8岁起开始在家自学,11岁赢得华盛顿州高中组科展大奖,成为历届年纪最小的大奖得主,并代表华盛顿州参加英特尔国际科展。12岁即进入华盛顿大学就读。除了医学外,徐安庐最关心的是世界上受压迫的儿童。他在11岁时与弟弟徐安祺共同创立了“世界儿童组织基金会”(Foundation for World Childern's Organization)关怀儿童教育问题;并结合专家学者完成一套共130册的英语教材,免费赠送各地贫童。美国CBS、ABC、《时代杂志》《、国家地理杂志》儿童版均曾报道徐安庐的故事,其学习经验被编入美国教科书中。展开更多
基金Supported by the National Natural Science Foundation of China(10371047)
文摘In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius, which improves some results in [4].
文摘15岁的徐安庐求学经历颇为传奇。两岁时以乐高组合玩具组成与自己同高的机器人,5岁时已能解简单的代数题目,6岁智商超出量表能测出的范围,8岁起开始在家自学,11岁赢得华盛顿州高中组科展大奖,成为历届年纪最小的大奖得主,并代表华盛顿州参加英特尔国际科展。12岁即进入华盛顿大学就读。除了医学外,徐安庐最关心的是世界上受压迫的儿童。他在11岁时与弟弟徐安祺共同创立了“世界儿童组织基金会”(Foundation for World Childern's Organization)关怀儿童教育问题;并结合专家学者完成一套共130册的英语教材,免费赠送各地贫童。美国CBS、ABC、《时代杂志》《、国家地理杂志》儿童版均曾报道徐安庐的故事,其学习经验被编入美国教科书中。
