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Search Results: 1 - 10 of 462002 matches for " A. Savas-Halilaj "
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Minimal graphs in $\mathbb{R}^{4}$ with bounded Jacobians
Th. Hasanis,A. Savas-Halilaj,Th. Vlachos
Mathematics , 2008,
Abstract: We obtain a Bernstein type result for entire two dimensional minimal graphs in $\mathbb{R}^{4}$, which extends a previous one due to L. Ni. Moreover, we provide a characterization for complex analytic curves.
Minimal hypersurfaces with zero Gauss-Kronecker curvature
T. Hasanis,A. Savas-Halilaj,T. Vlachos
Mathematics , 2004,
Abstract: We investigate complete minimal hypersurfaces in the Euclidean space $% \ {R}^{4}$, with Gauss-Kronecker curvature identically zero. We prove that, if $f:M^{3}\to {R}^{4}$ is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below, then $f(M^{3})$ splits as a Euclidean product $L^{2}\times {R}$, where $L^{2}$ is a complete minimal surface in $ {R}^{3}$ with Gaussian curvature bounded from below.
On the Jacobian of minimal graphs in R^4
Th. Hasanis,A. Savas-Halilaj,Th. Vlachos
Mathematics , 2009, DOI: 10.1112/blms/bdq105
Abstract: We provide a characterization for complex analytic curves among two-dimensional minimal graphs in $\mathbb{R}^{4}$ via the Jacobian
Complete minimal hypersurfaces of $S^4$ with zero Gauss-Kronecker curvature
T. Hasanis,A. Savas-Halilaj,T. Vlachos
Mathematics , 2004,
Abstract: We investigate the structure of 3-dimensional complete minimal hypersurfaces in the unit sphere with Gauss-Kronecker curvature identically zero.
Complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^4$ with vanishing Gauss-Kronecker curvature
T. Hasanis,A. Savas-Halilaj,T. Vlachos
Mathematics , 2005,
Abstract: We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below.
On Deformable Minimal Hypersurfaces in Space Forms
Andreas Savas-Halilaj
Mathematics , 2010,
Abstract: The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss-Kronecker curvature and scalar curvature bounded from below.
Evolution of contractions by mean curvature flow
Andreas Savas-Halilaj,Knut Smoczyk
Mathematics , 2013,
Abstract: We investigate length decreasing maps $f:M\to N$ between Riemannian manifolds $M$, $N$ of dimensions $m\ge 2$ and $n$, respectively. Assuming that $M$ is compact and $N$ is complete such that $$\sec_M>-\sigma\quad\text{and}\quad{\Ric}_M\ge(m-1)\sigma\ge(m-1)\sec_N\ge-\mu,$$ where $\sigma$, $\mu$ are positive constants, we show that the mean curvature flow provides a smooth homotopy of $f$ into a constant map.
The strong elliptic maximum principle for vector bundles and applications to minimal maps
Andreas Savas-Halilaj,Knut Smoczyk
Mathematics , 2012,
Abstract: Based on works by Hopf, Weinberger, Hamilton and Evans, we state and prove the strong elliptic maximum principle for smooth sections in vector bundles over Riemannian manifolds and give some applications in Differential Geometry. Moreover, we use this maximum principle to obtain various rigidity theorems and Bernstein type theorems in higher codimension for minimal maps between Riemannian manifolds.
Homotopy of area decreasing maps by mean curvature flow
Andreas Savas-Halilaj,Knut Smoczyk
Mathematics , 2013,
Abstract: Let $f:M\to N$ be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$. Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$, we prove that the mean curvature flow provides a smooth homotopy of $f$ to a constant map.
On the topology of translating solitons of the mean curvature flow
Francisco Martin,Andreas Savas-Halilaj,Knut Smoczyk
Mathematics , 2014,
Abstract: In the present article we obtain classification results and topological obstructions for the existence of translating solitons of the mean curvature flow.
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