查询词典 manifold without boundary

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

For an even dimensional compact oriented conformal real manifold without boundary, Connes has constructed a canonical Fredholm module and defined a conformal invariant by the Wodzicki residue.

对于偶数维、紧致、可定向、没有边界的共形实流形，Connes构造了一个标准的Fredholm模，并用Wodzicki留数定义了一个共形不变量。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。