The Hilbert area of inscribed triangles and quadrilaterals

Scott A. Wolpert

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arXiv · 2004.05432

The Hilbert area of inscribed triangles and quadrilaterals

Scott A. Wolpert

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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.

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Scott A. Wolpert. 2020-04-11. The Hilbert area of inscribed triangles and quadrilaterals. https://arxiv.org/abs/2004.05432

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