Minimal surfaces: A Lagrangian derivation of first and second variations

Key Points

• The aim is to establish a rigorous Lagrangian formulation for variational calculus applied to minimal surfaces.
• Developed a formulation using pullback covariant derivative.
• Utilized geometric arguments to show that all tangential variations vanish.
• Derived both first and second normal variations.
• Confirmed that all tangential variations are zero.
• Successfully derived first normal variations showing consistent results.
• Calculated second normal variations with established geometric principles.