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Index Estimates for Free Boundary f-minimal Hypersurfaces
We prove that the index is bounded from below by a linear function of its first Betti number for any compact free boundary f -minimal hypersurface in...
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A stability result for translating spacelike graphs in Lorentz manifolds
In this paper, we investigate spacelike graphs defined over a domain Ω ⊂ M n in the Lorentz manifold M n × ℝ with the metric −d s 2 + σ , where M n is a...
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Upper bound of Kähler angles on the β-symplectic critical surfaces
Let ( M , g ) be a Kähler surface and Σ be a β -symplectic critical surface in M . If L q (Σ) is bounded for some q > 3, then we give a uniform upper bound...
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Boundary Regularity for Minimal Graphs of Higher Codimensions
In this paper, the authors derive Hölder gradient estimates for graphic functions of minimal graphs of arbitrary codimensions over bounded open sets...
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A Simons-type Integral Inequality for Minimal Surfaces with Constant Kähler Angle in Complex Projective Spaces
In this paper, we establish a Simons-type integral inequality for minimal surfaces with constant Kähler angle in complex projective spaces, and we...
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Complete Self-similar Hypersurfaces to the Mean Curvature Flow with Nonnegative Constant Scalar Curvature
As is well known, self-similar solutions to the mean curvature flow, including self-shrinkers, translating solitons and self-expanders, arise...
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Left-Invariant Minimal Unit Vector Fields on the Solvable Lie Group
Božek (1980) has introduced a class of solvable Lie groups G n with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian...
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Global Rigidity Theorems for Submanifolds with Parallel Mean Curvature
In this paper, we mainly study the global rigidity theorem of Riemannian submanifolds in space forms. Let M n ( n ≥ 3) be a complete minimal submanifold...
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Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups
In this paper, the author computes canonical connections and Kobayashi-Nomizu connections and their curvature on three-dimensional Lorentzian Lie...
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A class of inverse quotient curvature flow in the AdS-Schwarzschild manifold
In this paper, we study the asymptotic behavior of a class of inverse quotient curvature flow in the anti-de Sitter-Schwarzschild manifold. We prove...
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Complete λ-Hypersurfaces in Euclidean Spaces
In this paper, the authors give a survey about λ-hypersurfaces in Euclidean spaces. Especially, they focus on examples and rigidity of...
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New Universal Inequalities for Eigenvalues of a Clamped Plate Problem
In this paper, we study the universal inequalities for eigenvalues of a clamped plate problem, and establish some new universal inequalities that are...
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Isoparametric Hypersurfaces Induced by Navigation in Lorentz Finsler Geometry
Using a navigation process with the datum ( F, V ), in which F is a Finsler metric and the smooth tangent vector field V satisfies F (− V ( x )) > 1...
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Characterizations of umbilic hypersurfaces in warped product manifolds
We consider the closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and...
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Minimal Legendrian surfaces in the tangent sphere bundle of ℝ3
In this paper, we study minimal Legendrian surfaces Σ immersed in the tangent sphere bundle T 1 ℝ 3 . We classify (1) totally geodesic Legendrian...