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One of the fundamental objects of study in geometric measure theory is an "area-minimizing surface." A compact, k-dimensional surface (with boundary) is called area-minimizing if no other surface with the same boundary has less surface area. An area-minimizing surface can have s…
Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis whose connections are usually not emphasized in introductory graduate courses. Yet one cannot dissociate the notions of mass or electric charge, naturally described in terms of meas…
