A note on \tmd-operator

2025/03/20 by Lin, Dexie, Zhou, Hengyu
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.15939

Abstract

In almost Kähler manifolds, one of the challenges is to construct an elliptic operator on functions that plays a role analogous to the ∂∂ operator in complex or Kähler manifolds. One of the aims of this paper is to revisit the \tmd-operator introduced in \citeTWZZ. We will provide some local analysis estimates and highlight several difficulties that remain to be addressed. Additionally, we use the Atiyah-Hitchin-Singer operator to demonstrate that every d-exact (1,1)-form is globally \tmd-exact for any compact taming symplectic 4-manifold.

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