Gradient estimates for Δ_b u + au^p+1 = 0 on pseudo-Hermitian manifolds

2024/08/27 by Biqiang Zhao, Zhao, Biqiang
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2408.14920

openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive the gradient estimates for the positive solutions of the equation Δ_b u + au^p+1 = 0 on complete noncompact pseudo-Hermitian manifolds, where a > 0 and p ≤ 0 or a < 0 and p > 0 are two constants. As an application, we will obtain a Liouville-type theorem when the manifolds are Sasakian-type with nonnegative pseudo-Hermitian Ricci curvature.

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