Weak elastic energy of rectifiable curves in the sphere

Key Points

• To introduce and analyze the p-curvature functional for rectifiable curves in the two-dimensional sphere.
• Defined the p-curvature functional for curves on a sphere.
• Proved finiteness of the functional for rectifiable curves.
• Established agreement with the integral of geodesic curvature in Sobolev space W2,p.
• The p-curvature functional is finite for rectifiable curves.
• It agrees with the integral of geodesic curvature raised to the power p for certain curves.