Year: 2026
Type: preprint
Abstract: We investigate the class of Liouville regular Jordan curves, which was introduced in our previous paper under the phrase "Jordan curves that admit continuous Legendrian lifts". We prove that a Jordan curve satisfying certain variation condition in a neighborhood of each point is in this class. We also prove that the boundary of a Jordan domain is Liouville regular if the images of the radial tails under a conformal mapping have uniformly vanishing length. Together with our previous result, these criteria imply the existence of an inscribed rectangle in every prescribed similarity class.
Source: arXiv (Cornell University)
Authors: Asano, Tomohiro, Ike, Yuichi
Institutions: Kyoto University, The University of Tokyo
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212269793
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