Work

Volume gap between the minimal submanifold and the unit sphere

Year: 2025

Type: article

Abstract: In 1984, Cheng et al. [Heat equations on minimal submanifolds and their applications, Amer. J. Math. 106(5) (1984) 1033–1065] proved that for a compact minimally immersed submanifold [Formula: see text] of [Formula: see text] there exists a positive constant [Formula: see text] depending only on [Formula: see text] such that [Formula: see text] In this paper, following the method of Cheng–Li–Yau, we first modify the coefficients in the constant [Formula: see text] to improve the volume gap. Further, we also enlarge our gap by applying an estimate of Cheng and Yang [Estimates on eigenvalues of Laplacian, Math. Ann. 331 (2005) 445–460] for eigenvalues of Laplacian.

Source: International Journal of Mathematics

DOI: 10.1142/s0129167x25500296

Authors: Weiran Ding, Jianquan Ge, Fagui Li

Institutions: Beijing Normal University, Beijing Institute of Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, Fundamental Research Funds for the Central Universities

Awards: G1700875239, G4485653004