Extremal Surfaces of Limit Curvature at Critical Points. The Cornu Scroll as an Extremal Geometric Surface of Infinite Curvature: The Analytical Paradox of Asymptotic Divergence of the Surface Measure in a Bounded Domain in the Neighborhood of the Singularity Points.

Key Points

• This work aims to explore the geometric features of the Cornu scroll as an extremal surface and the related paradoxes of surface measure behavior.
• Analyzed the characteristics of the 3D Cornu scroll surface.
• Investigated the surface measure divergence around singularity points in a bounded spatial domain.
• Identified analytical paradox related to surface measure divergence.
• Proposed important implications for understanding extremal surfaces in geometry.