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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2013, Issue 685


Higher genus minimal surfaces in S3 and stable bundles

Sebastian Heller
Published Online: 2012-03-09 | DOI: https://doi.org/10.1515/crelle-2012-0011


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.

About the article

Received: 2010-08-23

Revised: 2011-12-30

Published Online: 2012-03-09

Published in Print: 2013-12-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2013, Issue 685, Pages 105–122, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2012-0011.

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