Guang, QiangLi, Qi RuiWang, Xu Jia2025-05-232025-05-230022-040Xhttp://www.scopus.com/inward/record.url?scp=85186498576&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733751950Given a function f > 0 on the unit sphere Sn+1, the Minkowski problem in the sphere concerns the existence of convex hypersurfaces M ⊂ Sn+1 such that the Gauss curvature of M at z is equal to f(ν(z)), where ν(z) is the unit outer normal of M at z. We use the min-max principle and the Gauss curvature flow to prove that there are at least two solutions to the problem. By using the rotating plane method in the sphere, we also show the existence of a rotationally symmetric and monotone function f such that there are exactly two solutions.Acknowledgments. Li\u2019s research was supported by National Key R&D Program of China (no. 2022YFA1005500), NSFC (no. 12031017), and Zhejiang Provincial NSFC (no. LR23A010002). Guang\u2019s research was supported by ARC DE210100535. Wang\u2019s research was supported by ARC DP200101084.49enPublisher Copyright: © 2024 International Press, Inc.. All rights reserved.202410.4310/jdg/172771289285186498576