| The goal of this thesis is to introduce the method of universal pseudoholomorphic pullback equations and apply it in some situations to construct and classify pseudoholomorphic curves into the symplectizations of closed threemanifolds with an almost complex structure adjusted to a trivializable contact structure. For these almost complex structures, the existence of pseudoholomorphic curves is equivalent to the existence of a special point on the manifold called a closing point. The task of proving the existence of closing points and classifying finite energy pseudoholomorphic curves will be initiated, but the task is not completed in this thesis.;The task of constructing pseudoholomorphic curves into these symplectizations is separated into an analytic part and a topological part. The analytic part requires proving the existence of a pair of (1, 0)-forms (α, β) satisfying a nonlinear perturbed Cauchy-Riemann system on the complex plane with regular singularities, polar boundary conditions, and a boundary relation. These solution pairs are studied by introducing weighted singular Floer operators on model domains, using index theory, and studying some nonlinear problems. The topological part requires integrating the solution pairs under the assumption that closing points exist and then demonstrating the existence of closing points. |
