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Graphs with parallel mean curvature
We prove that if the graph Ff = {(x, f(x)): x E M} of a map f: (M, g) -(N, h) between Riemannian manifolds is a submanifold of (M x N, g x h) with parallel mean curvature H, then on a compact domainExpand
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Spacelike graphs with parallel mean curvature
We consider spacelike graphs $\Gamma_f$ of simple products $(M\times N, g\times -h)$ where $(M,g)$ and $(N,h)$ are Riemannian manifolds and $f:M\to N$ is a smooth map. Under the condition of theExpand
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Grassman manifolds as subsets of Euclidean spaces
Let E be a Euclidean space. Following Palais, we identify each vector subspace F of E with the orthogonal projection πF : E → F . In this way, the Grassman manifold G(E) of all vector subspaces of EExpand
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Graphic Bernstein results in curved pseudo-Riemannian manifolds
Abstract We generalize a Bernstein-type result due to Albujer and Alias, for maximal surfaces in a curved Lorentzian product 3-manifold of the form Σ 1 × R , to higher dimension and codimension. WeExpand
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Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds
Given a manifold $$M$$M, we build two spherically symmetric model manifolds based on the maximum and the minimum of its curvatures. We then show that the first Dirichlet eigenvalue of theExpand
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Mean curvature flow of spacelike graphs
We prove the mean curvature flow of a spacelike graph in (Σ1 × Σ2, g1 − g2) of a map f : Σ1 → Σ2 from a closed Riemannian manifold (Σ1, g1) with Ricci1 > 0 to a complete Riemannian manifold (Σ2, g2)Expand
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On the spectrum of $\bar{X}$-bounded minimal submanifolds
We prove, under a certain boundedness condition at infinity on the $(\bar{X}^{\top}, \bar{X}^{\bot})$-component of the second fundamental form, the vanishing of the essential spectrum of a completeExpand
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Forced convex mean curvature flow in Euclidean spaces
We show the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term may shrink to a point in finite time if the forcing term is small, or exist for all times andExpand
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Dirichlet principal eigenvalue comparison theorems in geometry with torsion
This work was supported by the Fundacao para a Ciencia e Tecnologia (Portugal) through the project PTDC/MAT/118682/2010, and through Centro de Matemtica da Universidade do Minho Expand
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Fe b 20 06 Spacelike graphs with parallel mean curvature
We consider spacelike graphs Γf of simple products (M × N, g × −h) where (M, g) and (N, h) are Riemannian manifolds and f : M → N is a smooth map. Under the condition of the Cheeger constant of M toExpand
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