The asymptotic behavior of a finite energy plane
The asymptotic behavior of a finite energy plane
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有限能量平面的渐近行为
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
E. Zehnder
中科院分区：
文献类型：
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作者：
H. Hofer;K. Wysocki;E. Zehnder
给定具有接触形式λ的紧致3流形M，我们考虑求解Cauchy-Riemann方程Tu i = J(u) Tu的光滑映射u: C→R ×M，对于R ×M上与λ相关的一类R不变的几乎复杂结构J。如果映射是非常数且能量有限，则M的投影必然趋近于与接触形式相关的Reeb向量场的周期解|z|→∞。假设周期解是非退化的，我们将描述映射u的渐近行为。本文是[5]的修订版本，并且还包括[6]。
Given a compact 3-manifold M equipped with the contact form λ we consider smooth maps u : C → R × M solving the Cauchy-Riemann equations Tu i = J(u) Tu, for a distinguished class of almost complex structures J on R ×M which are R-invariant and related to λ. If the map is non constant and of finite energy, the projection into M necessarily approaches as |z| → ∞ a periodic solution of the Reeb vector field associated with the contact form. Assuming the periodic solution to be non degenerate we shall describe the asymptotic behavior of the map u. The paper is a revised version of [5] and includes also [6].