Simons-type equation for \(f\)-minimal hypersurfaces and applications
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Publication:253836
DOI10.1007/s12220-014-9530-1zbMath1344.53043arXiv1305.2379OpenAlexW2097132000MaRDI QIDQ253836
Detang Zhou, Tito Mejia, Xu Cheng
Publication date: 8 March 2016
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1305.2379
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)
Related Items (24)
\(L_{f}\)-index bounds for closed \(f\)-minimal hypersurfaces ⋮ Stability properties and gap theorem for complete \(f\)-minimal hypersurfaces ⋮ Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold ⋮ Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons ⋮ Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons ⋮ Uniqueness of grim hyperplanes for mean curvature flows ⋮ Remarks on mean curvature flow solitons in warped products ⋮ The self-shrinker in warped product space and the weighted Minkowski inequality ⋮ Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian ⋮ Mean curvature flow in an extended Ricci flow background ⋮ \(\lambda\)-Hypersurfaces on shrinking gradient Ricci solitons ⋮ Harmonic 1-forms on minimal hypersurfaces in \(\mathbb{S}^n \times \mathbb{R}\) ⋮ Rigidity results and topology at infinity of translating solitons of the mean curvature flow ⋮ Index and first Betti number of \(f\)-minimal hypersurfaces: general ambients ⋮ Minimal submanifolds in a metric measure space ⋮ Stable and isoperimetric regions in some weighted manifolds with boundary ⋮ Vanishing properties of -minimal hypersurfaces in a complete smooth metric measure space ⋮ Geometric properties of self-shrinkers in cylinder shrinking Ricci solitons ⋮ Spectral properties and rigidity for self-expanding solutions of the mean curvature flows ⋮ \(L^{2p}_f\)-harmonic 1-forms on \(f\)-minimal hypersurfaces in a weighted manifold ⋮ The rigidity and stability of complete 𝑓-minimal hypersurfaces in ℝⁿ×𝕊¹(𝕒) ⋮ Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces ⋮ Dirichlet problem for \(f\)-minimal graphs ⋮ $F$-stability of $f$-minimal hypersurface
Cites Work
- Stability properties and gap theorem for complete \(f\)-minimal hypersurfaces
- Flow by mean curvature inside a moving ambient space
- Generic mean curvature flow. I: Generic singularities
- Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers
- Mean curvature flow in a Ricci flow background
- Eigenvalue estimate and compactness for closed \(f\)-minimal surfaces
- Asymptotic behavior for singularities of the mean curvature flow
- On complete minimal surfaces with finite Morse index in three manifolds
- Curvature estimates for minimal hypersurfaces
- A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
- \(f\)-minimal surface and manifold with positive \(m\)-Bakry-Émery Ricci curvature
- Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor
- Minimal varieties in Riemannian manifolds
- Volume estimate about shrinkers
- Stability and compactness for complete 𝑓-minimal surfaces
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