A Wolpert Theorem for shearing coordinates

A theorem from Wolpert bounds the Weil--Petersson distance from a hyperbolic surface to a maximally noded surface in terms of the lengths of the underlying pants decomposition. We prove analogues for punctured surfaces both in terms of the lambda-lengths and in terms of the shearing coordinates of an ideal triangulation.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-03
DOI
https://doi.org/10.48550/arxiv.2611.05045
Primary Topic
Geometric and Algebraic Topology
Type
preprint
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preprint

A Wolpert Theorem for shearing coordinates

Marie Abadie
arXiv (Cornell University)
Geometric and Algebraic Topology
preprint

A Wolpert Theorem for shearing coordinates

Marie Abadie
preprint en

Abstract

A theorem from Wolpert bounds the Weil--Petersson distance from a hyperbolic surface to a maximally noded surface in terms of the lengths of the underlying pants decomposition. We prove analogues for punctured surfaces both in terms of the lambda-lengths and in terms of the shearing coordinates of an ideal triangulation.

arXiv (Cornell University)
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
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A Wolpert Theorem for shearing coordinates — Marie Abadie · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS