Invariant probability measures from pseudoholomorphic curves II: Pseudoholomorphic curve constructions

2021/08/31 by Rohil Prasad, Prasad, Rohil
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2109.00106

openalex publication_date 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the previous work, we introduced a method for constructing invariant probability measures of a large class of non-singular volume-preserving flows on closed, oriented odd-dimensional smooth manifolds with pseudoholomorphic curve techniques from symplectic geometry. The technique requires existence of certain pseudoholomorphic curves satisfying some weak assumptions. In this work, we appeal to Gromov-Witten theory and Seiberg-Witten theory to construct large classes of examples where these pseudoholomorphic curves exist. Our argument uses neck stretching along with new analytical tools from Fish-Hofer's work on feral pseudoholomorphic curves.

Related

• Invariant probability measures from pseudoholomorphic curves I
• Some Questions in the Theory of Pseudoholomorphic Curves
• Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm
• Pseudo-rotations and holomorphic curves
• Pseudoholomorphic curves in four-orbifolds and some applications