Limit Polygons of Convex Domains in the Projective Plane

DOI10.1093/IMRN/RNAA259zbMATH Open1504.53023arXiv1912.02060OpenAlexW3091207424MaRDI QIDQ5068149

Xin Nie

Publication date: 5 April 2022

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: For any sequence of properly convex domains in the real projective plane such that the zeros of Pick differentials have bounded multiplicity and get further and further apart, we determined all Hausdorff limit domains that one can obtain after normalizing each member of the sequence by a projective transformation. We then show that the result can be applied to convex domains generated by projective triangular reflection groups.

Full work available at URL: https://arxiv.org/abs/1912.02060

zbMATH Keywords

Blaschke metricconvex domainsPick differentialprojective triangular reflection groupsWang's developing mapWang's equation

Mathematics Subject Classification ID

Projective differential geometry (53A20) Affine differential geometry (53A15)

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