Extremal length in higher dimensions and complex systolic inequalities
Complex Variables
2020-06-26 v4 Differential Geometry
Abstract
Extremal length is a classical tool in 1-dimensional complex analysis for building conformal invariants. We propose a higher-dimensional generalization for complex manifolds and provide some ideas on how to estimate and calculate it. We also show how to formulate certain natural geometric inequalities concerning moduli spaces in terms of a complex analogue of the classical Riemannian notion of systole.
Keywords
Cite
@article{arxiv.1904.07807,
title = {Extremal length in higher dimensions and complex systolic inequalities},
author = {Tommaso Pacini},
journal= {arXiv preprint arXiv:1904.07807},
year = {2020}
}
Comments
Contains improved presentation of complex systolic inequalities and comparisons with special Lagrangian geometry. Various other minor changes. To appear in Journal of Geometric Analysis