Multiple Solutions to the Planar Plateau Problem
Matthias Schneider
TL;DR
This paper investigates the existence and nonuniqueness of simple planar curves with specified geodesic curvature, providing new insights into the solutions of the planar plateau problem.
Contribution
It establishes both existence and nonuniqueness results for curves with prescribed geodesic curvature, advancing understanding of the planar plateau problem.
Findings
Existence of solutions for prescribed geodesic curvature.
Nonuniqueness of solutions under certain conditions.
New methods for analyzing planar curves with curvature constraints.
Abstract
We give existence and nonuniqueness results for simple planar curves with prescribed geodesic curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering