Spectral flow, Llarull's rigidity theorem in odd dimensions and its generalization

作     者：Yihan Li Guangxiang Su Xiangsheng Wang 

作者机构：Chern Institute of Mathematics&LPMCNankai UniversityTianjin 300071China School of MathematicsShandong UniversityJinan 250100China 

出 版 物：《Science China Mathematics》 (中国科学（数学）（英文版）)

年 卷 期：2024年第67卷第5期

页      面：1103-1114页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by Nankai Zhide Foundation supported by National Natural Science Foundation of China(Grant Nos.12271266 and 11931007) supported by National Natural Science Foundation of China(Grant No.12101361) Nankai Zhide Foundation the Fundamental Research Funds for the Central Universities(Grant No.100-63233103) the Project of Young Scholars of Shandong University the Fundamental Research Funds of Shandong University(Grant No.2020GN063) 

主　　题：Dirac operator scalar curvature spectral flow 

摘      要：For a compact spin Riemannian manifold(M,g^(TM))of dimension n such that the associated scalar curvature kT M verifies that k^(TM)≥n(n-1),Llarull’s rigidity theorem says that any area-decreasing smooth map f from M to the unit sphere Sn of nonzero degree is an *** this paper,we present a new proof of Llarull’s rigidity theorem in odd dimensions via a spectral flow *** approach also works for a generalization of Llarull’s theorem when the sphere Sn is replaced by an arbitrary smooth strictly convex closed hypersurface in Rn+*** results answer two questions by Gromov(2023).