(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

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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.

(Elsevier B.V., 2005-07-14) Dorfmeister, J.; Kilian, Martin; Engineering and Physical Sciences Research Council

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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.

(Mathematical Society of Japan, 2013-07) Kilian, Martin; Schmitt, Nicholas

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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.

(Osaka University and Osaka Metropolitan University, Departments of Mathematics, 2012-09) Kilian, Martin

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We discuss constant mean curvature bubbletons in Euclidean 3-space via dressing with simple factors, and prove that single-bubbletons are not embedded.