一个在保高斯映射共形形变下的整体不变量

设Ｘ：Ｍｎ →ＥＮ 为黎曼流形（Ｍｎ ，ｇ）到欧氏Ｎ—空间的等距浸入，＜ ｈ ＞ 及Ｈ 分别表示浸入Ｘ 的第二基本形式的长度及平均曲率，本文将证明积分∫Ｍ ｎ ＜ ｈ ＞ ｎｄｖ 在保高斯映射的共形形变下是不变量。如果ｎ ＝ ２，Ｘ 为紧嵌入，那么积分∫Ｍ ２ Ｈ２ ｄｖ 在上述形变下是不变量。本文也给出一个Ｅ３ 中可保高斯映射共形形变的紧曲面的唯一性定理。

Global Well-Posedness of Incompressible Navier-Stokes Equations with Two Slow Variables

In this paper, the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach.