Ramified optimal transportation in geodesic metric spaces

DOI10.1515/ACV.2011.002zbMath1223.49053arXiv0907.5596MaRDI QIDQ3086997

Qinglan Xia

Publication date: 1 August 2011

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.5596

zbMATH Keywords

curvaturedoubling spaceoptimal transport pathramified optimal transportationbranching structuredimension of measures

Mathematics Subject Classification ID

Transportation, logistics and supply chain management (90B06) Variational problems in a geometric measure-theoretic setting (49Q20) Nonstandard measure theory (28E05)

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On landscape functions associated with transport paths ⋮ A mass reducing flow for real-valued flat chains with applications to transport networks

Cites Work

• The geodesic problem in quasimetric spaces
• Optimal transportation networks as flat chains
• Path functionals over Wasserstein spaces
• The geometry of optimal transportation
• Size minimization and approximating problems
• A variational model of irrigation patterns
• Rectifiability of flat chains
• Interior regularity of optimal transport paths
• Regularity of potential functions of the optimal transportation problem
• Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
• On the Transport Dimension of Measures
• The formation of a tree leaf
• OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS

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