Gluing Techniques in Calibrated Geometry

of the Dissertation Gluing Techniques in Calibrated Geometry by Yongsheng Zhang Doctor of Philosophy in Mathematics Stony Brook University 2013 This thesis is concerned with the question: given a submanifold (perhaps with singularities), when is it possible to change the metric in some specific way so that the submanifold becomes homologically mass-minimizing? We studied this question for “horizontal” change of metrics and conformal change of metrics for both compact and non-compact submanifolds. We also explored cases with singularities or boundaries. The main idea is to use the theory of calibrated geometry and gluing techniques. As a special case, we confirm that any given oriented compact