论文标题
在更高维度中
Conformal geometry, Euler numbers, and global invertibility in higher dimensions
论文作者
论文摘要
结果表明，在至少三个尺寸中，欧几里得n空间的局部差异为本身就是射层，前提是每个平面的下拉是一个riemannian submanifold，它与平面是一致的。使用类似的技术，当且仅当每个复杂线的撤回背包都是连接的有理曲线时，就可以恢复结果，即复合$ n $空间的多项式本地局部生物形态可逆。这些结果是我们主要定理的特殊情况，其证明使用几何形状，复杂的分析，椭圆形偏微分方程和拓扑。
It is shown that in dimension at least three a local diffeomorphism of Euclidean n-space into itself is injective provided that the pull-back of every plane is a Riemannian submanifold which is conformal to a plane. Using a similar technique one recovers the result that a polynomial local biholomorphism of complex $n$-space into itself is invertible if and only if the pull-back of every complex line is a connected rational curve. These results are special cases of our main theorem, whose proof uses geometry, complex analysis, elliptic partial differential equations, and topology.
