Annales Fennici Mathematici· 2026Q1
Schoenflies problem for area-preserving biLipschitz mappings
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- Q1SCImago
- 2026year
Short summary
Any biLipschitz mapping of the unit disk boundary to a domain boundary of equal area can be extended to an area-preserving biLipschitz mapping of the entire plane.
AI-generated from the title and abstract; the full text is not read.
Key points
- BiLipschitz mappings of disk boundaries with equal area are considered.
- The mapping can be extended to the entire plane.
- The extended mapping is biLipschitz and area-preserving.
- This addresses a version of the Schoenflies problem for area-preserving maps.
AI-generated from the title and abstract; the full text is not read.
Abstract
We prove that any biLipschitz mapping of the boundary of the unit disk onto the boundary of the domain of the same area can be extended to a biLipschitz mapping of the whole plane which preserves the area of any measurable subset.
The authors' abstract, as published at the source. Annales Fennici Mathematici, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics