Almost complex rigidity of the complex projective plane

Castelnuovo's bound and rigidity in almost complex geometry

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.

关于接近极小值的哈密顿量刚性的研究，及其在磁系统和近凯勒流形中的应用

On the Rigidity of Hamiltonians which are Zoll Near a Minimum, with an Application to Magnetic Systems and Almost-Kähler Manifolds

研究接近极小值的哈密顿系统，证明在能量水平序列趋近极小值时，哈密顿量的Hessian与辛结构的限制相容，且在磁系统中，度量与磁形式相容，定义了近凯勒结构，揭示了复空间形式的动态特征。