Gupta, Subhojoy and Wolf, Michael
(2016)
*Quadratic differentials, half-plane structures, and harmonic maps to trees.*
In: COMMENTARII MATHEMATICI HELVETICI, 91
(2).
pp. 317-356.

## Abstract

Let (Sigma, p) be a pointed Riemann surface and k >= 1 an integer. We parametrize the space of meromorphic quadratic differentials on Sigma with a pole of order k + 2 at p, having a connected critical graph and an induced metric composed of k Euclidean half-planes. The parameters form a finite-dimensional space L similar or equal to R-k x S-1 that describe a model singular-flat metric around the puncture with respect to a choice of coordinate chart. This generalizes an important theorem of Strebel, and associates, to each point in T-g,T- 1 x L, a unique metric spine of the surface that is a ribbon-graph with k infinite-length edges to p. The proofs study and relate the singular-flat geometry of the quadratic differential, and the infinite-energy harmonic map from Sigma \textbackslash p to a k-pronged tree, having the same Hopf differential.

Item Type: | Journal Article |
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Publication: | COMMENTARII MATHEMATICI HELVETICI |

Publisher: | EUROPEAN MATHEMATICAL SOC |

Additional Information: | Copy right for this article belongs to the EUROPEAN MATHEMATICAL SOC, PUBLISHING HOUSE, E T H-ZENTRUM SEW A27, SCHEUCHZERSTRASSE 70, CH-8092 ZURICH, SWITZERLAND |

Keywords: | Meromorphic differentials; singular-flat metrics; Riemann surfaces; harmonic maps |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 11 Jun 2016 09:53 |

Last Modified: | 11 Jun 2016 09:53 |

URI: | http://eprints.iisc.ac.in/id/eprint/53930 |

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