Uniqueness of tangent cones for semicalibrated integral 2-cycles

Abstract

Semicalibrated currents in a Riemannian manifold are currents that are calibrated by a comass-$1$ differential form that is not necessarily closed. This extension of the classical notion of calibrated currents is motivated by important applications in differential geometry such as special Legendrian currents, for example. We prove that semicalibrated integer multiplicity rectifiable $2$-cycles have a unique tangent cone at every point. The proof is based on the introduction of a new technique that might be useful for other first-order elliptic problems