1) 3 sphere theorem
三球定理
1.
The author gives out a curvature condition about the asymptotic Dirichlet problems on higher dimensional rotational Mfd,and extend the Hardmard 3 sphere theorem in complex analysis to general Riemannian Mtd which leading to a Liouville type theorem,at last,use the method due to L.
给出了高维旋转对称流形上Δｕ＝０的渐近Ｄｉｒｉｃｈｌｅｔ边值问题可解的一个曲率条件，且将Ｈａｒｄａｍａｒｄ三球定理推广到一般Ｒｉｅｍａｎｎｉａｎ流形上，并导出一个相应的Ｌｉｏｕｖｉｌｅ型结果，最后用Ｌ。
2) three spheres theorem
三球面定理
1.
Hadamand′s three spheres theorem for p-harmonic equations;
p-调和方程的Hadamand三球面定理
3) Hadamard's three-spheres theorems
Hadamard三球面定理
4) Sphere theorem
球定理
1.
A sphere theorem of Riemannian manifolds with little negative curvature;
具有小负曲率黎曼流形的球定理
2.
We derive a new proof of a sphere theorem whenever the manifold concerned satisfies that the sectional curvature K_M is not larger than 1,while Ric(M)≥(n+2)/4 and the volume V(M) is not larger than 3/2(1+η)V(S~(2n)) for some positive numberηdepending only on n.
最终将给出一个具有正的Ricci曲率的球定理新证明。
3.
" A sphere theorem with a pinching constant below 1/4 ", which appeared in Journal of Differential Geometry, by U.
球定理一直是整体微分几何中的核心问题，并且由它推动了比较几何中大量问题的发展，产生了许多新的思想和方法，已经构成了微分几何中最强大的分支之一。
5) three link theorem
三心定理
1.
The limitation of three link theorem in velocity analysis and the main problems in application of Lou s theorem are pointed out.
指出了用于速度分析的三心定理的局限性，应用罗洪田定式应注意的一些问题。
6) three-solution theorem
三解定理
1.
Some new three-solution theorems are employed to discuss the problem.
通过应用一个新的三解定理,得到了边值问题多重正解的存在性。
2.
By using a new three-solution theorem,we obtain the existence and multiplicity of positive solutions for fourth-order boundary value problem.
讨论了四阶边值问题,通过应用一个新的三解定理,得到了其解的存在性与多重性。
3.
By using the fixed point theory and a new three-solution theorems,the existence of multiple solutions of the boundary value problem was obtained.
通过利用不动点指数理论及一个新的三解定理,得到了边值问题多个正解的存在性。
补充资料：三垂线定理的逆定理
Image:11732716937617776.jpg
三垂线定理的逆定理
在平面内的一条直线，如果它和这个平面的一条斜线垂直，那么它也和这条斜线在平面内的射线垂直。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。