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Complete Constant Mean Curvature Hypersurfaces in Euclidean space of dimension four or higher. (arXiv:1707.04008v1 [math.DG])
来源于:arXiv
In this article we provide a general construction when $n\ge3$ for immersed
in Euclidean $(n+1)$-space, complete, smooth, constant mean curvature
hypersurfaces of finite topological type (in short CMC $n$-hypersurfaces). More
precisely our construction converts certain graphs in Euclidean $(n+1)$-space
to CMC $n$-hypersurfaces with asymptotically Delaunay ends in two steps: First
appropriate small perturbations of the given graph have their vertices replaced
by round spherical regions and their edges and rays by Delaunay pieces so that
a family of initial smooth hypersurfaces is constructed. One of the initial
hypersurfaces is then perturbed to produce the desired CMC $n$-hypersurface
which depends on the given family of perturbations of the graph and a small in
absolute value parameter $\underline\tau$. This construction is very general
because of the abundance of graphs which satisfy the required conditions and
because it does not rely on symmetry requirements. For any given $k\ge2$ 查看全文>>