论文标题
分析通过涡度封闭的可定向表面上的体积保留差异组的指数图
On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity
论文作者
论文摘要
我们通过不可压缩的Euler方程的涡度制定，研究了封闭的可定向表面上的体积保护差异的指数图。我们提出了ebin-misiołek定理的替代性，流体动力学证明 - 普雷斯顿：指数是指数零的非线性弗雷德·霍尔姆映射。我们将指数图的Shnirelman的刚度结果从二维平面圆环扩展到了可定向的封闭表面。也就是说，我们证明了指数图是弗雷德·古尔姆·Quasiregular。
We study the exponential map of group of volume-preserving diffeomorphisms on closed orientable surfaces via the vorticity formulation of the incompressible Euler equation. We present an alternative, fluid dynamical proof of the theorem of Ebin--Misiołek--Preston: the exponential is a nonlinear Fredholm mapping of index zero. We extend Shnirelman's rigidity result for the exponential map from 2-dimensional flat torus to arbitrary orientable closed surfaces. That is, we prove that the exponential map is Fredholm quasiregular.
