Smooth homeomorphic approximation of piecewise affine homeomorphisms
Daniel Campbell, Filip Soudsk\'y

TL;DR
This paper presents a method to approximate any piecewise affine homeomorphism with a smooth injective map in the Sobolev space, ensuring the approximation is arbitrarily close in the $W^{1,p}$ norm.
Contribution
It introduces a technique to smoothly approximate piecewise affine homeomorphisms while preserving injectivity and controlling the approximation error.
Findings
Successfully approximates piecewise affine homeomorphisms with smooth injective maps
Ensures the approximation error can be made arbitrarily small in the Sobolev norm
Maintains the homeomorphic property in the approximation process
Abstract
Given any a locally finitely piecewise affine homeomorphism of onto in , and any we construct a smooth injective map such that .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic and geometric function theory · Meromorphic and Entire Functions · Fixed Point Theorems Analysis
