Iteration Formulae for Brake Orbit and Index Inequalities for Real Pseudoholomorphic Curves

Fredholm Theory for Pseudoholomorphic Curves with Brake Symmetry

In this paper we study pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudoholomorphic curve with brake symmetry and the corresponding moduli space. Then we get the virtual dimension of the moduli space.

接触瞬子与辛化上伪全纯曲线的渐近算子微扰理论

Perturbation theory of asymptotic operators of contact instantons and pseudoholomorphic curves on symplectization

本文为接触瞬子和辛化上伪全纯曲线的渐近算子建立精确张量公式，并提出相容CR近复结构变化下的微扰理论，填补了文献空白，同时利用特征值与特征向量简化了穿孔处精细渐近行为的研究。

Analysis of pseudoholomorphic curves on symplectization: Revisit via contact instantons

In this survey article, we present the analysis of pseudoholomorphic curves $u:(\dot Σ,j) \to (Q \times \mathbb{R}, \widetilde J)$ on the symplectization of contact manifold $(Q,λ)$ as a subcase of the analysis of contact instantons $w:\dot Σ\to Q$, i.e., of the maps $w$ satisfying the equation $$ {\bar{\partial}}^πw = 0, \, d(w^*λ\circ j) = 0 $$ on the contact manifold $(Q,λ)$, which has been carried out by a coordinate-free covariant tensorial calculus. When the analysis is applied to that of pseudoholomorphic curves $u = (w,f)$ with $w = π_Q \circ u$, $f = s\circ u$ on symplectization, the …