调和函数 meaning in English
ellipsoidal harmonics
harmonic function
harmonics
Examples
- In chapter 3 , we will estimate the first eigenvalue of laplacian from below on manifolds with a little negative curvature . in chapter 4 , we will prove the existence of bounded nontrivial harmonic functions on some classes of complete manifolds which will generalize the results of s . y . cheng ' s
在第三章，我们将给出具有小负曲率的流形上laplace算子的第一特征值的下界估计；第四章，我们会给出一类完备非紧流形上非平凡的有界调和函数的存在性，推广了s . y . cheng的结果。 - The article stated here will give some remarks to the following equation in two cases : for the case > 0 , the equation expresses the eigenvalue of the laplacian while for the case = 0 , it is the existence of nontriv - ial bounded harmonic functions on complete noncompact manifolds
本文中我们主要分两种情况来讨论了关于laplace算子的方程： u + u = 0 ， r ~ + { 0 }对应于0 ，是riemann流形上laplace算子的特征值问题，而对应于= 0则是完备非紧流形上非平凡的有界调和函数的存在性问题。