Polyharmonic Almost Complex Structures

2019/09/22 by Weiyong He, He, Weiyong, Ruiqi Jiang +1 · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1909.09959

Abstract

In this paper we consider the existence and regularity of weakly polyharmonic almost complex structures on a compact almost Hermitian manifold M^2m. Such objects satisfy the elliptic system weakly [J, Δ^m J]=0. We prove a very general regularity theorem for semilinear systems in critical dimensions (with critical growth nonlinearities). In particular we prove that weakly biharmonic almost complex structures are smooth in dimension four.

Cited by

• Quantitative stratification and optimal regularity for harmonic almost complex structures

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