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The Spinor Representation Of Surfaces In Space, Robert Kusner, Nick Schmitt
The Spinor Representation Of Surfaces In Space, Robert Kusner, Nick Schmitt
Robert Kusner
The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan [32], which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the canonical line bundle K = T(M). Given a conformal immersion of M into R3, the unique spin strucure on S2 pulls back via the Gauss map to a spin structure S on M, and gives rise to a pair of smooth sections (s1, s2) of S. Conversely, any pair of sections of S generates a (possibly periodic) conformal immersion …
Moduli Spaces Of Embedded Constant Mean Curvature Surfaces With Few Ends And Special Symmetry, Karsten Grosse-Brauckmann, Robert Kusner
Moduli Spaces Of Embedded Constant Mean Curvature Surfaces With Few Ends And Special Symmetry, Karsten Grosse-Brauckmann, Robert Kusner
Robert Kusner
We give necessary conditions on complete embedded cmc surfaces with three or four ends subject to reflection symmetries. The respective submoduli spaces are twodimensional varieties in the moduli spaces of general cmc surfaces. We characterize fundamental domains of our cmc surfaces by associated great circle polygons in the three-sphere.
The Moduli Space Of Complete Embedded Constant Mean Curvature Surfaces, Robert Kusner, Rafe Mazzeo, Daniel Pollack
The Moduli Space Of Complete Embedded Constant Mean Curvature Surfaces, Robert Kusner, Rafe Mazzeo, Daniel Pollack
Robert Kusner
We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of all such surfaces with k ends (where surfaces are identified if they differ by an isometry of $\RR^{3}$) is locally a real analytic variety. When the linearization of the quasilinear elliptic equation specifying mean curvature equal to one has no L2−nullspace we prove that $\Mk$ is locally the quotient of a real analytic manifold of dimension 3k−6 by a finite group …