A homotopy formula for a_q domains in complex manifolds

2025/03/29 by Gong, Xianghong, Shi, Ziming
#32A26 #32F10 #32W05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.22953

Abstract

We construct a global homotopy formula for a_q domains in a complex manifold. The homotopy operators in the formula will gain 1/2 derivative in Hölder-Zygmund spaces Λ^r when the boundaries of the domains are in Λ^r+3 with r>0.

Related

• Hölder estimates for homotopy operators on strictly pseudoconvex domains with C² boundary
• Occupants in manifolds
• On ∂ homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates
• Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds
• Solving Homotopy Domain Equations