2001
DOI: 10.4310/cag.2001.v9.n1.a6
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Constant mean curvature surfaces with Delaunay ends

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Cited by 95 publications
(143 citation statements)
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“…In the case of complete noncompact constant mean curvature surfaces, the moduli space of such surfaces is now fairly well understood (in the genus 0 case). Then, many examples of such surfaces are produced in [9] and [16] and a classification of embedded constant mean curvature surfaces with three ends is given in [3]. However, the set of compact constant mean curvature is not so well understood.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…In the case of complete noncompact constant mean curvature surfaces, the moduli space of such surfaces is now fairly well understood (in the genus 0 case). Then, many examples of such surfaces are produced in [9] and [16] and a classification of embedded constant mean curvature surfaces with three ends is given in [3]. However, the set of compact constant mean curvature is not so well understood.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%
“…The analogue of the following result for n = 2 is usually know as the "Linear Decomposition Lemma" (see [17] and [16]). …”
Section: Annales De L'institut Fouriermentioning
confidence: 99%
“…They have been used to understand solutions to problems arising from the geometry (minimal and constant mean curvature surfaces [13,14], constant scalar curvature metrics [9,12,15], and recently even Einstein metrics [1]) and from the physic (Einstein constraint equations [7] and [8]). However most of the results are concerned with the connected sum at points (point-wise connected sum), whereas the case of connected sum along a submanifold (generalized connected sum or fiber sum) has received less attention.…”
Section: Introduction and Statement Of The Resultsmentioning
confidence: 99%
“…The collection of properly embedded CM C surfaces with bounded second fundamental form is quite large and varied (see [4,10,11,15,16,17]). Many of these examples appear as doubly and singly-periodic surfaces.…”
Section: Introductionmentioning
confidence: 99%
“…Many of these examples appear as doubly and singly-periodic surfaces. The techniques of Kapouleas [10] and MazzeoPacard [16] can be applied to obtain many nonperiodic examples of finite and infinite topology. Some theoretical aspects of the study of these special surfaces have been developed previously in works of Meeks [18], Korevaar-Kusner-Solomon [13] and Korevaar-Kusner [12]; results from all of these three key papers are applied here.…”
Section: Introductionmentioning
confidence: 99%