Minimal Surfaces of Revolution

We consider the minimal surface problem for surfaces of revolution. If the meridian curves are in arclength parameter, then the geodesic equations can be reduced to a nonlinear second order differential equation. This class of differential equations (ones with the independent variable missing) can be solved by introducing a new variable. We solve the minimal surface equation and show that the only minimal surface of revolution is a catenoid.
#mikethemathematician, #profdabkowski, #mikedabkowski, #differentialgeometry, #minimalsurface