Planar Immersions with Prescribed Curl and Jacobian Determinant are Unique

TL;DR

This paper proves that in two dimensions, immersions are uniquely determined by their Jacobian determinant, curl, and boundary data, resolving a key conjecture in grid generation for computer graphics.

Contribution

It establishes the uniqueness of planar immersions based on Jacobian, curl, and boundary conditions, addressing a longstanding conjecture in the field.

Findings

Immersions are uniquely determined by Jacobian, curl, and boundary data.

Resolves the two-dimensional case of a major conjecture in grid generation.

Provides theoretical foundation for improved grid generation methods.

Abstract

We prove that immersions of planar domains are uniquely specified by their Jacobian determinant, curl function, and boundary values. This settles the two-dimensional version of an outstanding conjecture related to a particular grid generation method in computer graphics.