Computing the Conformal Barycenter

DOI10.1137/21M1449282WikidataQ114073966 ScholiaQ114073966MaRDI QIDQ5039488

Henrik Schumacher, Jason Cantarella

Publication date: 13 October 2022

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.03958

zbMATH Keywords

polygon spaceDouady-Earle extensionconformal barycenterRiemannian Newton methodRiemannian Newton-Kantorovich theorem

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computational methods for problems pertaining to differential geometry (53-08) Numerical methods in conformal mappings (65E10)

Cites Work

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• The symplectic geometry of polygons in Euclidean space
• Conformal barycenters and the Douady-Earle extension -- a discrete dynamical approach.
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• A unique representation of polyhedral types. Centering via Möbius transformations
• Conformally natural extension of homeomorphisms of the circle
• A Kähler structure on the moduli space of isometric maps of a circle into Euclidean space
• Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
• Open and closed random walks with fixed edgelengths in $ \newcommand{\m}{\mathcal} \newcommand{\R}{\mathbb{R}} \R^d$
• The Hopf-Rinow Theorem is false in infinite Dimensions
• Complexity of the Regularized Newton Method

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