A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces

DOI10.1090/proc/15835zbMath1489.53089OpenAlexW4200250562MaRDI QIDQ3390671

Fagui Li, Jian Quan Ge

Publication date: 25 March 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/15835

zbMATH Keywords

minimal hypersurfaceintegral inequalitypinching theoremPerdomo conjecture

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Integral geometry (53C65) Rigidity results (53C24)

Related Items (2)

A note on the Chern conjecture in dimension four ⋮ Weighted monotonicity theorems and applications to minimal surfaces of ℍⁿ and 𝕊ⁿ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Errata to: ``Isoparametric hypersurfaces with \((g,m)=(6,2)\)
• Isoparametric hypersurfaces with four principal curvatures. III.
• Isoparametric foliation and Yau conjecture on the first eigenvalue
• Embedded minimal tori in \(S^3\) and the Lawson conjecture
• \(n\)-dimensional area of minimal rotational hypersurfaces in spheres
• Sharp lower bounds on density for area-minimizing cones
• On Chern's problem for rigidity of minimal hypersurfaces in the spheres
• On minimal hypersurfaces with constant scalar curvatures in \(S^ 4\)
• Low index minimal hypersurfaces of spheres
• Minimal cones and the spherical Bernstein problem. I
• A first eigenvalue estimate for minimal hypersurfaces
• Global pinching theorems for even dimensional minimal submanifolds in the unit spheres
• Chern's conjecture on minimal hypersurfaces
• On CMC hypersurfaces in \(\mathbb{S}^{n+1}\) with constant Gauß-Kronecker curvature
• On the average of the scalar curvature of minimal hypersurfaces of spheres with low stability index
• The scalar curvature of minimal hypersurfaces in spheres
• Rigidity of minimal hypersurfaces of spheres with two principal curvatures
• \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
• Isoparametric hypersurfaces with \((g,m)=(6,2)\)
• On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere
• Isoparametric hypersurfaces with four principal curvatures. IV
• A sufficient condition for a hypersurface to be isoparametric
• Closed Willmore minimal hypersurfaces with constant scalar curvature in \(\mathbb{S}^5(1)\) are isoparametric
• On the classification of isoparametric hypersurfaces with four distinct curvatures in spheres
• On Chern's conjecture for minimal hypersurfaces and rigidity of self-shrinkers
• Isoparametric hypersurfaces with four principal curvatures
• Isoparametric foliation and Yau conjecture on the first eigenvalue. II.
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Minimal immersions of surfaces in Euclidean spheres
• Local rigidity theorems for minimal hypersurfaces
• Minimal varieties in Riemannian manifolds
• On the Gauss mapping for hypersurfaces of constant mean curvature in the sphere
• The unknottedness of minimal embeddings
• Closed 3-dimensional hypersurfaces with constant mean curvature and constant scalar curvature
• Area of minimal hypersurfaces in the unit sphere
• Geometry of Hypersurfaces
• Isoparametric hypersurfaces with four principal curvatures, II
• Chern conjecture and isoparametric hypersurfaces
• The pinching constant of minimal hypersurfaces in the unit spheres
• First eigenvalue of symmetric minimal surfaces in $\mathbb{S}^3$
• Heat Equations on Minimal Submanifolds and Their Applications
• Isoparametric hypersurfaces, case g=6, m=1
• A characterization of the Clifford torus
• A Global Pinching Theorem of Minimal Hypersurfaces in the Sphere
• A spectral characterization of the $H(r)$-torus by the first stability eigenvalue
• Minimal surfaces in $$S^3$$ : a survey of recent results
• THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE
• On the stability index of hypersurfaces with constant mean curvature in spheres
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
• The Isoparametric Story, a Heritage of \'{E}lie Cartan
• Scalar curvature of minimal hypersurfaces in a sphere

This page was built for publication: A lower bound for 𝐿₂ length of second fundamental form on minimal hypersurfaces