Definition:Mean Curvature

Definition

Let $C$ be a curve defined by a real function which is twice differentiable.

Let $\delta \psi$ be the angle of contingence with respect to $2$ points $P$ and $Q$ on $C$.

Let $\delta s$ be the arc length of $C$ between $P$ and $Q$.

The mean curvature of $C$ between $P$ and $Q$ is defined as $\dfrac {\delta \psi} {\delta s}$.

Also see

• Results about mean curvature can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): curvature