Reference book: John Oprea, Differential Geometry and its applications,
Prentice Hall, 1997
Euler-Lagrange equations (variational principle): p.257
Further reading: Pontryagin Maximum Principle p.297.
Applications : level sets, snakes, physical simulation
Demo: surface Evolver.
3D surfaces to get 2D properties : Level Sets methods (transition)
Eric Amram, Feb 1998, MIT 6.838 Advanced Topics in Computer
Graphics - Prof. Seth Teller.