A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds
A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds
复制标题
DOI：
10.1007/s00526-003-0212-2
复制
发表时间：
2005-05-01
影响因子：
2.1
通讯作者：
Chow, B
中科院分区：
文献类型：
--
作者：
Anderson, G;Chow, B
证明了闭三维流形上线性化Ricci流系统解的一个估计。这个估计是对具有正Ricci曲率的三维流形上Ricci流解的Ricci曲率的汉密尔顿的pinching估计的推广。在我们的估计中，我们对初始度量的曲率没有任何假设。我们表明，规范的解决方案的Lichnerowicz拉普拉斯热方程（耦合到里奇流）是有界的常数（取决于时间）倍的标量曲率加上一个常数。这依赖于Bochner型公式，并建立6个变量的4次齐次多项式的非负性。
We prove an estimate for solutions to the linearized Ricci flow system on closed 3-manifolds. This estimate is a generalization of Hamilton's pinching is preserved estimate for the Ricci curvatures of solutions to the Ricci flow on 3-manifolds with positive Ricci curvature. In our estimate we make no assumption on the curvature of the initial metric. We show that the norm of the solution of the Lichnerowicz Laplacian heat equation (coupled to the Ricci flow) is bounded by a constant (depending on time) times the scalar curvature plus a constant. This relies on a Bochner type formula and establishing the nonnegativity of a degree 4 homogeneous polynomial in 6 variables.