论文标题
将定理在完整的Riemannian歧管上，具有非负RICCI曲率
Splitting theorems on complete Riemannian manifolds with nonnegative Ricci curvature
论文作者
论文摘要
在本文中，我们对具有非负RICCI曲率的完整riemannian歧管提供了一些局部和全球分裂的结果。我们通过分析Modica类型的某些点不平等的分析来实现分裂，这些不平等是针对半线性泊松方程的每个有界解决方案所致。更确切地说，我们证明存在非构构界解决方案$ u $的存在，在某个时候，以前的不平等中的一种成为平等，导致了分裂结果以及对这种解决方案$ u $的分类。
In this paper we provide some local and global splitting results on complete Riemannian manifolds with nonnegative Ricci curvature. We achieve the splitting through the analysis of some pointwise inequalities of Modica type which hold true for every bounded solution to a semilinear Poisson equation. More precisely, we prove that the existence of a nonconstant bounded solution $u$ for which one of the previous inequalities becomes an equality at some point leads to the splitting results as well as to a classification of such a solution $u$.
