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A rigidity theorem for self-expanders
In this paper, we completely classify 3-dimensional complete self-expanders with constant squared norm S of the second fundamental form and constant $...
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Classification of complete 3-dimensional self-shrinkers in the Euclidean space ℝ4
In this paper, we completely classify 3-dimensional complete self-shrinkers with the constant norm S of the second fundamental form and the constant f3 in the Euclidean space ℝ4, where hij’s are components of the...
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An Immersed \(S^{n}\) \(\lambda \) -Hypersurface
In this paper, we construct an immersed, non-embedded \(S^{n}\) S
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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 λ-hypersurfaces in Euclidean spaces.
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Complete Lagrangian self-shrinkers in \({\mathbf {R}}^4\)
The purpose of this paper is to study complete self-shrinkers of mean curvature flow in Euclidean spaces. In the paper, we give a complete classification for 2-dimensional complete Lagrangian self-shrinkers in...
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Some Log-Minkowski Inequalities for (p, q)-Mixed Volume
The notion of (p, q)-mixed volume was introduced by Lutwak, Yang and Zhang. In this paper, associated with the (p, q)-mixed volume, we prove a modification of the log-Minkowski inequality which is a unification f...
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Complete self-shrinkers with constant norm of the second fundamental form
In this paper, we classify 3-dimensional complete self-shrinkers in Euclidean space \({\mathbb {R}}^{4}\) ...
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Some log-Minkowski inequalities for \(L_p\) -mixed affine surface area
In this paper, we define the \(L_p\) L p ...
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Complete \(\lambda \) -surfaces in \({\mathbb {R}}^3\)
The purpose of this paper is to study complete \(\lambda \) λ -surfaces in E...
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Examples of compact λ-hypersurfaces in Euclidean spaces
In this paper, we first construct compact embedded λ-hypersurfaces with the topology of torus which are called λ-torus in Euclidean spaces ℝn+1. Then, we give many compact immersed λ-hypersurfaces in Euclidean sp...
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Complete \(\lambda \) -hypersurfaces of weighted volume-preserving mean curvature flow
In this paper, we introduce a special class of hypersurfaces which are called \(\lambda \) ...
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On Variational Formulas of a Conformally Invariant Functional
We consider a conformally invariant functional of the space of Riemannian metrics, compute its first variational formula and obtain some examples of its critical point. Then we compute the second variation of ...
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A Characterization of Quadric Constant Scalar Curvature Hypersurfaces of Spheres
Let M⊂S 4 be a complete orientable hypersurface with constant scalar curvature. For any v∈R 5, let us define the two real functions
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A class of minimal Lagrangian submanifolds in complex hyperquadrics
In this paper we construct a class of compact minimal Lagrangian submanifolds in complex hyperquadrics by studying Gauss maps of compact rotational hypersurfaces in the unit sphere.
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A lower bound for eigenvalues of a clamped plate problem
In this paper, we study eigenvalues of a clamped plate problem. We obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter.
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Estimates for lower order eigenvalues of a clamped plate problem
For a bounded domain Ω in a complete Riemannian manifold M n , we study estimates for lower order eigenvalues of a clamped plate problem. We obtain unive...
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Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space H 1 n+1 (−1)
In this paper, we study closed k-maximal spacelike hypersurfaces M n in anti-de Sitter space H 1 ...
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Compact embedded rotation hypersurfaces of Sn+1
In this paper, we prove that $$ S^{{n - 1}} {\left( {{\sqrt {\frac{{n - m}} {n}} }} \right)} \times S^{1} {\left( {{\sqrt {\frac{m} {n...
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Rigidity Theorem for Hypersurfaces in a Unit Sphere
By investigating hypersurfaces M n in the unit sphere S n+1(1) with H ...
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Complete Hypersurfaces with Constant Mean Curvature in a Unit Sphere
By investigating hypersurfaces M n in the unit sphere S n+1(1) with constant mean curvature and with...
