scholarly journals $F$-stability of $f$-minimal hypersurface

2015 ◽  
Vol 143 (8) ◽  
pp. 3619-3629 ◽  
Author(s):  
Weimin Sheng ◽  
Haobin Yu
Keyword(s):  
Minimal Hypersurface

scholarly journals On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard Manifold

2017 ◽  
Vol 47 (4) ◽  
pp. 485-501 ◽  
Author(s):  
Jean-Baptiste Casteras ◽  
Ilkka Holopainen ◽  
Jaime B. Ripoll
Keyword(s):  
Dirichlet Problem ◽  
Minimal Hypersurface ◽  
Hadamard Manifold

THE SCALAR CURVATURE OF MINIMAL HYPERSURFACES IN A UNIT SPHERE

2007 ◽  
Vol 09 (02) ◽  
pp. 183-200 ◽  
Author(s):  
YOUNG JIN SUH ◽  
HAE YOUNG YANG
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Constant Scalar Curvature ◽  
Minimal Hypersurface ◽  
Second Fundamental Form ◽  
Geodesic Sphere ◽  
Clifford Torus ◽  
Totally Geodesic ◽  
Minimal Hypersurfaces ◽  
The Second Fundamental Form

In this paper, we study n-dimensional compact minimal hypersurfaces in a unit sphere Sn+1(1) and give an answer for S. S. Chern's conjecture. We have shown that [Formula: see text] if S > n, and prove that an n-dimensional compact minimal hypersurface with constant scalar curvature in Sn+1(1) is a totally geodesic sphere or a Clifford torus if [Formula: see text], where S denotes the squared norm of the second fundamental form of this hypersurface.

Plateau-Stein manifolds

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Misha Gromov
Keyword(s):  
Finite Volume ◽  
Riemannian Manifolds ◽  
Critical Points ◽  
Minimal Hypersurface ◽  
Proper Function ◽  
Stein Manifolds ◽  
Morse Functions ◽  
Complete Riemannian Manifolds

AbstractWe study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

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