The Hilbert area of inscribed triangles and quadrilaterals
Geometric Topology
2020-12-21 v3 Metric Geometry
Abstract
Hilbert volume is an invariant of real projective geometry. Polygons inscribed in polygons are considered for the real projective plane. The correspondence between Fock-Goncharov and Cartesian coordinates is examined. Degeneration and Hilbert area of inscribed quadrilaterals are analyzed. A microlocal condition is developed for bounded Hilbert area under degeneration. The condition is applied to give a sequence of strictly convex domains with bounded Hilbert area and divergent Goldman parameters.
Keywords
Cite
@article{arxiv.2004.05432,
title = {The Hilbert area of inscribed triangles and quadrilaterals},
author = {Scott A. Wolpert},
journal= {arXiv preprint arXiv:2004.05432},
year = {2020}
}
Comments
17 pages, 4 figures. Version 2 has an expanded introduction discussing the established results in the literature. Version 3 has small additions to explanations