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arXiv · 2512.01751

From pre-lamination to foliated plane

Christian Bonatti·Théo Marty
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Abstract

To a singular foliation on the plane corresponds a circular boundary at infinity endowed with a pre-lamination on the circle. We solve the converse direction. We determine which pre-lamination on the circle are boundary at infinity of a foliation, and we build the corresponding (unique) foliation. We consider both regular foliations and a singular foliations with prong singularities.

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Christian Bonatti, Théo Marty. 2025-12-01. From pre-lamination to foliated plane. https://arxiv.org/abs/2512.01751

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