Gupta, Subhojoy and Wolf, Michael (2017) Meromorphic quadratic differentials with complex residues and spiralling foliations. [Book Chapter]
Full text not available from this repository.Abstract
A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential at the pole. We introduce the space of such measured foliations, and prove that for a fixed Riemann surface, any such foliation is realized by a quadratic differential with second order poles at marked points. Furthermore, such a differential is uniquely determined if one prescribes complex residues at the poles that are compatible with the transverse measures around them. This generalizes a theorem of Hubbard and Masur concerning holomorphic quadratic differentials on closed surfaces, as well as a theorem of Strebel for the case when the foliation has only closed leaves. The proof involves taking a compact exhaustion of the surface, and considering a sequence of equivariant harmonic maps to real trees that do not have a uniform bound on total energy.
| Item Type: | Book Chapter |
|---|---|
| Publisher: | American Mathematical Society |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 03 Jun 2022 05:25 |
| Last Modified: | 03 Jun 2022 05:25 |
| URI: | https://eprints.iisc.ac.in/id/eprint/73057 |
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