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Higher genus minimal surfaces in S3 and stable bundles
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Sebastian Heller
Published/Copyright:
March 9, 2012
Abstract.
We consider compact minimal surfaces 
of genus 2 which are homotopic to an embedding. We prove that such surfaces
can be constructed from a globally defined family of meromorphic connections by the DPW method.
The poles of the meromorphic connections are at the Weierstrass points of the Riemann surface and are at most quadratic. For the existence proof
of the DPW potential, we give a characterization of stable extensions 
of spin bundles S by its dual 
in terms of an associated element of 
. We also show that the family of holomorphic structures associated to a minimal surface of genus 
in S3 is generically stable.
Received: 2010-08-23
Revised: 2011-12-30
Published Online: 2012-03-09
Published in Print: 2013-12-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Existence and uniqueness of constant mean curvature spheres in
- Nilpotent operators and weighted projective lines
- Variation of the canonical height for a family of polynomials
- Purity for Pfister forms and F4-torsors with trivial g3 invariant
- Higher genus minimal surfaces in S3 and stable bundles
- Minimal surfaces with limit ends in
- Special points on fibered powers of elliptic surfaces
- A motivic conjecture of Milne
