109 research outputs found

    Higher dimensional Scherk's hypersurfaces

    Get PDF
    In 3-dimensional Euclidean space, Scherk second surfaces are singly periodic embedded minimal surfaces with four planar ends. In this paper, we obtain a natural generalization of these minimal surfaces in any higher dimensional Euclidean space Rn+1{\R}^{n+1}, for n≥3n \geq 3. More precisely, we show that there exist (n−1)(n-1)-periodic embedded minimal hypersurfaces with four hyperplanar ends. The moduli space of these hypersurfaces forms a 1-dimensional fibration over the moduli space of flat tori in Rn−1{\R}^{n-1}. A partial description of the boundary of this moduli space is also given.Comment: 22 pages. Improved versio

    Attaching handles to Delaunay nodo\"{\i}ds

    Full text link
    For all m∈N−{0}m \in \mathbb N - \{0\}, we prove the existence of a one dimensional family of genus mm, constant mean curvature (equal to 1) surfaces which are complete, immersed in R3\mathbb R^3 and have two Delaunay ends asymptotic to nodo\"{\i}dal ends. Moreover, these surfaces are invariant under the group of isometries of R3\mathbb R^3 leaving a horizontal regular polygon with m+1m+1 sides fixed

    Blowing up and desingularizing constant scalar curvature K\"{a}hler manifolds

    Full text link
    This paper is concerned with the existence of constant scalar curvature Kaehler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kaehler metrics. We also consider the desingularization of isolated quotient singularities of compact orbifolds which already carry constant scalar curvature Kaehler metrics.Comment: Greatly revised version. 43 page
    • …
    corecore