Work

On open manifolds admitting no complete metric with positive scalar curvature

Year: 2026

Type: article

Abstract: In this paper, we investigate the topological obstruction problem for positive scalar curvature and uniformly positive scalar curvature on open manifolds. We present a definition for open Schoen–Yau–Schick manifolds and prove that there is no complete metric with positive scalar curvature on these manifolds. Similarly, we define weak Schoen–Yau–Shick manifolds by analogy, which are expected to admit no complete metrics with uniformly positive scalar curvature.

Source: Annales de l’institut Fourier

DOI: 10.5802/aif.3762

Authors: Yuguang Shi, Jian Wang, Runzhang Wu, Jintian Zhu

Institutions: Peking University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Stony Brook University, Westlake University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Westlake University, Banff International Research Station for Mathematical Innovation and Discovery

OpenAlex ID: W7140911369