2022/12/15 by Xiangzhi Cao, Cao, Xiangzhi
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2212.07831
openalex publication_date 2022/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly derive monotonicity formula of generalized map using conservation law, including ϕ-F harmonic map coupled with ϕ-F symphonic map with m form and potential from metric measure space, p harmonic map with potential , V harmonic map with potential. As an corollary, we can derive Liouville theorem for these maps under some finite energy conditons. We also get Liouville type theorem for ϕ-F harmonic map coupled with ϕ-F symphonic map under asymptotic conditon on metric measure space. We also get Liouville theorem for ϕ-F-V-harmonic maps in terms of the upper bound of Ricci curvature and the bound about sectional curvature on metric measure space. We also get Liouville theorem for ϕ- F -harmonic map without using monotonicity formula on metric measure space.