Corpus ID: 119052775

Doubling and Desingularization Constructions for Minimal Surfaces

  title={Doubling and Desingularization Constructions for Minimal Surfaces},
  author={N. Kapouleas},
  journal={arXiv: Differential Geometry},
  • N. Kapouleas
  • Published 2010
  • Mathematics
  • arXiv: Differential Geometry
In the first part of the paper we discuss the current status of the application of the gluing methodology to doubling and desingularization constructions for minimal surfaces in Riemannian three-manifolds. In particular a doubling construction for equatorial spheres in $S^3(1)$ is announced. Aspects of the current understanding of existence and uniqueness questions for closed minimal embedded surfaces in $S^3(1)$ are also discussed, and some new uniqueness questions are proposed. In the second… Expand
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