Analysis Seminar

Calibrated currents are a particular class of volume-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 smoothness properties of calibrated currents play a key role. After a review of some known smoothness results I will present an "infinitesimal regularity" result, namely on the uniqueness of tangent cones for pseudo-holomorphic currents.