2017/11/18 by Jhovanny Muñoz Posso, Posso, Jhovanny Muñoz
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1711.06876
openalex publication_date 2017/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Yamabe problem in compact closed Riemannian manifolds is concerned with finding a metric with constant scalar curvature in the conformal class of a given metric. This problem was solved by the combined work of Yamabe, Trudinger, Aubin, and Schoen. In particular, Aubin solved the case when the Riemannian manifold is compact, is nonlocally conformally flat and has a dimension equal to or greater than 6. In 2015, Case considered a Yamabe-type problem in the setting of smooth measure space in manifolds and for a parameter m, which generalizes the original Yamabe problem when m=0. Additionally, Case solved this problem when the parameter m is a natural number. In the context of the Yamabe-type problem, we generalize Aubin's result for nonlocally conformally flat manifolds, with dimension equal and greater than 6 and parameter m close to nonnegative integers.