# Parabolic stable surfaces with constant mean curvature

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We study surfaces defined as graph of the function z = f(x, y) in the product space â„2 Ã— â„. In particular, we completely classify flat or minimal surfaces given by f(x, y) = u(x) + V(y), where u(x) and V(y) are smooth functions.

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Extending the work of G. SzÃ©kelyhidi and T. Br Ã¼onnle to Sasakian manifolds, we prove that a small deformation of the complex structure of the cone of a constant scalar curvature Sasakian (cscS) manifold admits a constant scalar curvature structure if it is K-polystable. This also implies...

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We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and nonnegative Ricci curvature. Conversely, for a class of surfaces possessing a simple...

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In this paper, we investigate the properties of small surfaces of Willmore type in three-dimensional Riemannian manifolds. By small surfaces, we mean topological spheres contained in a geodesic ball of small enough radius. In particular, we show that if there exist such surfaces with positive...

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In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular...

- On Graphs, Which Can be Drawn on an Orientable Surface with Small Number of Intersections on an Edge. Samoilova, O. // Journal of Mathematical Sciences;Feb2016, Vol. 212 Issue 6, p714
Let k and g be nonnegative integers. A graph is said to be k-nearly g-spherical if it can be drawn on an orientable surface of genus g so that each edge intersects at most k other edges in interior points. It is proved that if k â‰¤ 4 , then the edge number of a k-nearly g-spherical graph on...