Vanishing properties of -minimal hypersurfaces in a complete smooth metric measure space

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Spectral theory; eigenvalue problems on manifolds (58C40)

Cites Work

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Simons-type equation for \(f\)-minimal hypersurfaces and applications
\(L^2\)-harmonic 1-forms on submanifolds with finite total curvature
Vanishing theorems for \(L^2\) harmonic 1-forms on complete submanifolds in a Riemannian manifold
Stability properties and topology at infinity of \(f\)-minimal hypersurfaces
\(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds
Comparison geometry for the Bakry-Emery Ricci tensor
Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces
\(L^{2}\) harmonic 1-forms on minimal submanifolds in hyperbolic space
The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
Some geometric properties of the Bakry-Émery-Ricci tensor
Total scalar curvature and \(L^2\) harmonic 1-forms on a minimal hypersurface in Euclidean space
Rigidity of minimal submanifolds in hyperbolic space
Ricci curvature for metric-measure spaces via optimal transport
Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor
On the geometry of metric measure spaces. I
On the geometry of metric measure spaces. II
\(L^p\) harmonic \(1\)-forms and first eigenvalue of a stable minimal hypersurface
Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold
Harmonic forms on manifolds with non-negative Bakry-Émery-Ricci curvature
Stable complete minimal surfaces in 𝑅³ are planes
Stability and compactness for complete 𝑓-minimal surfaces

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