几乎复几何中的Castelnuovo界与刚性
Castelnuovo's bound and rigidity in almost complex geometry
摘要：
本文研究了殆复流形中伪全纯曲线的能量界是否蕴含亏格界的问题。在回顾了6维以外的维中的已知情况后，我们在6维中建立了一个新的结果，特别是对于辛卡-丘6维流形。证明依赖于J-全纯流的紧性和正则性定理。
英文摘要：
This article is concerned with the question of whether an energy bound implies a genus bound for pseudo-holomorphic curves in almost complex manifolds. After reviewing what is known in dimensions other than 6, we establish a new result in this direction in dimension 6; in particular, for symplectic Calabi-Yau 6-manifolds. The proof relies on compactness and regularity theorems for J-holomorphic currents.
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