A quote from Danny Calegari's lecture notes about minimal surfaces:
"A critical point for a smooth function on a finite dimensional manifold is usually called stable when the Hessian (i.e. the matrix of second partial derivatives) is positive definite. This ensures that the point is an isolated local minimum for the function. However, in minimal surface theory one says that minimal submanifolds are stable when the second variation is merely non-negative..."
Is there a reason for the deviating terminology?