10/7/2011

Costante Bellettini
Princeton University

Calibrated currents in geometry

Calibrated currents are a particular class of mass-minimizers and as such provide interesting explicit examples of solutions to Plateau?s problem. Their role goes however much beyond that: they naturally appear when dealing with several geometric questions. After a brief introduction to currents and calibrations, we will overview some geometric problems where the regularity of calibrated currents plays a key role. Then we will present two such results, one for Special Lagrangian 3-dimensional integral cones (joint work with T. Rivière) and an "infinitesimal regularity" result for non-rectifiable pseudo-holomorphic 2-dimensional currents