2022/03/12 by Valter Borges, Borges, Valter
Mathematics · #53C20 #53C21 #53C25 #53C44 #58J60 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2203.06441
openalex publication_date 2022/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this article is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain pde estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.