Mathematical Sciences- Journal Articles

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    Constant mean curvature surfaces of any positive genus
    (Cambridge University Press, 2005-07-20) Kilian, Martin; Kobayashi, S.-P.; Rossman , W.; Schmitt, N.; Ministry of Education, Culture, Sports, Science and Technology; Deutsche Forschungsgemeinschaft; Engineering and Physical Sciences Research Council
    The paper shows the existence of several new families of noncompact constant mean curvature surfaces: (i) singly punctured surfaces of arbitrary genus g 1, (ii) doubly punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.
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    Dressing preserving the fundamental group
    (Elsevier B.V., 2005-07-14) Dorfmeister, J.; Kilian, Martin; Engineering and Physical Sciences Research Council
    In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non-finite type cylinders.
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    Constant mean curvature trinoids with one irregular end
    (Tohoku University, Mathematical Institute, 2020-06-26) Kilian, Martin; Mota, Eduardo; Schmitt, Nicholas
    We construct a new five parameter family of constant mean curvature trinoids with two asymptotically Delaunay ends and one irregular end.
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    Constant mean curvature cylinders with irregular ends
    (Mathematical Society of Japan, 2013-07) Kilian, Martin; Schmitt, Nicholas
    We prove the existence of a new class of constant mean curvature cylinders with an arbitrary number of umbilics by unitarizing the monodromy of Hill's equation.
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    Bubbletons are not embedded
    (Osaka University and Osaka Metropolitan University, Departments of Mathematics, 2012-09) Kilian, Martin
    We discuss constant mean curvature bubbletons in Euclidean 3-space via dressing with simple factors, and prove that single-bubbletons are not embedded.