The minima of a flow named for one form of this quantity solve the isoperimetric problem. The local form of one theorem relates the sum of exterior angles of a simple surface to the sum of integrals of two forms of this quantity, and the global form relates those integrals to the Euler characteristic. As the Hessian's eigenvalues give a form of this quantity, the Hessian's determinant at extrema determines a function's concavity. Under an arc length parametrization, this quantity is the magnitude of the derivative of the tangent vector. For 10 points, name this measure of a surface's bending.
The minima of a flow named for one form of this quantity solve the isoperimetric problem. The local form of one theorem relates the sum of exterior angles of a simple surface to the sum of integrals of two forms of this quantity, and the global form relates those integrals to the Euler characteristic. As the Hessian's eigenvalues give a form of this quantity, the Hessian's determinant at extrema determines a function's concavity. Under an arc length parametrization, this quantity is the magnitude of the derivative of the tangent vector. For 10 points, name this measure of a surface's bending.
The minima of a flow named for one form of this quantity solve the isoperimetric problem.