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arXiv · 2204.09497

On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity

Siran Li
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Abstract

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--Misio\l{}ek--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.

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Siran Li. 2022-04-20. On analysis of the exponential map of volume-preserving diffeomorphism group on closed orientable surfaces through the vorticity. https://arxiv.org/abs/2204.09497

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