Mean curvature

Mean curvature is a way to measure how a surface bends at a specific point. Imagine a surface like a soap bubble or a curved piece of fabric. At any point, the surface can bend in different directions. Mean curvature averages these bending behaviors, capturing whether the surface is bulging outward, inward, or flat locally. If the mean curvature is zero, the surface is perfectly balanced, like a minimal surface. Positive or negative values indicate bending in specific ways. Overall, mean curvature helps describe the shape and stability of curved surfaces in geometry and physics.