Invariant probability measures from pseudoholomorphic curves II: Pseudoholomorphic curve constructions
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.
Cite
@article{arxiv.2109.00106,
title = {Invariant probability measures from pseudoholomorphic curves II: Pseudoholomorphic curve constructions},
author = {Rohil Prasad},
journal= {arXiv preprint arXiv:2109.00106},
year = {2021}
}
Comments
87 pages, 8 figures. v2: Updated references to the prequel. Minor language/typo cleanup. Submitted