An Obstruction to the Existence of Immersed Curves of Prescribed Curvature

TL;DR

The paper investigates the existence of immersed curves with prescribed curvature and demonstrates obstructions to their existence under certain conditions.

Contribution

It provides new theoretical results showing conditions that prevent the existence of immersed curves with specific curvature functions.

Findings

Identifies obstructions to immersed curves of prescribed curvature.

Establishes conditions under which such curves cannot exist.

Contributes to the understanding of geometric constraints on curves.

Abstract

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