Calibrated geometry is a concept in differential geometry that deals with certain types of geometric structures, specifically those that can be associated with calibration forms. A calibration is a differential form that can be used to define a notion of volume in a geometric setting, helping to identify and characterize minimal submanifolds.
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Calibrated geometry constructs volume-minimizing submanifolds through closed differential forms with a tangent-plane bound. It gives an algebraic sufficient condition for solving the nonlinear minimal surface problem.