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Scalar curvature, volume, and Weil-Petersson translation length
Abstract
We construct metrics on pseudoAnosov mapping tori that make every fiber an intrinsically hyperbolic stable minimal surface, and which have scalar curvature identically -6. Using this, we give a new proof (with improved constant) of an inequality bounding the hyperbolic volume of a pseudoAnosov mapping torus by the Weil-Petersson translation length (and consequently, the entropy) of its monodromy.
Related
- Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
- Integral of Scalar Curvature under Volume Collapse
- Volume Entropy and Scalar Curvature near a Hyperbolic Metric
- An improved volume bound under Ricci and scalar curvature lower bounds
- Comparison between renormalized volume and area in the Weil--Petersson topology
BibTeX
@misc{rudd2026scalar,
title = {{Scalar curvature, volume, and Weil-Petersson translation length}},
author = {Cameron Gates Rudd},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21885},
eprint = {2610.21885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21885},
}
RIS
TY - UNPB
TI - Scalar curvature, volume, and Weil-Petersson translation length
AU - Cameron Gates Rudd
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21885
UR - https://arxiv.org/abs/2610.21885
AB - We construct metrics on pseudoAnosov mapping tori that make every fiber an intrinsically hyperbolic stable minimal surface, and which have scalar curvature identically -6. Using this, we give a new proof (with improved constant) of an inequality bounding the hyperbolic volume of a pseudoAnosov mapping torus by the Weil-Petersson translation length (and consequently, the entropy) of its monodromy.
ER -