Simons' type equation for f-minimal hypersurfaces and applications

2013/05/10 by Xu Cheng, Cheng, Xu, Tito Mejia +3 · 1 citation
Mathematics · #49Q05 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1305.2379

openalex publication_date 2013/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the Simons' type equation for f-minimal hypersurfaces in weighted Riemannian manifolds and apply it to obtain a pinching theorem for closed f-minimal hypersurfaces immersed in the product manifold \mathbbSⁿ(√(2(n-1)))× ℝ with f=\frac t²4. Also we classify closed f-minimal hypersurfaces with L_f-index one immersed in \mathbbSⁿ(√(2(n-1)))× ℝ with the same f as above.

Cited by

• On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends

Related

• Curvature estimates for minimal hypersurfaces
• Simons' equation and minimal hypersurfaces in space forms
• The existence of embedded minimal hypersurfaces
• The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
• A lower bound for L₂ length of second fundamental form on minimal hypersurfaces