A Pseudo-gradient Flow Arising In Contact Form Geometry

作者：Xu, Yongzhong^*

来源：Advanced Nonlinear Studies, 2015, 15(2): 447-496.

DOI：10.1515/ans-2015-0210

• contact form
• pseudo-gradient flow
• Legendrian loops
• variational problem

In this work we construct a pseudo-gradient flow on a subspace C-beta of the dual Legendrian curves on a closed contact 3-manifold. These results improve and refine earlier results proved in this framework by A. Bahri [3]. The variational problem involved is not compact, thus asymptotes and critical points at infinity might occur. The flow in this work deforms curves in C-beta into a special set boolean OR(k is an element of N)Gamma(2k) of curves at infinity and thus allows us a better understanding of this non-compact problem.

• 出版日期2015-5
• 单位上海交通大学