Bakri Gad Elseed Rahmat Alla Mohammed2017-08-022017-08-022015http://hdl.handle.net/123456789/4603Abstract This research is concerned with geometric measure theory. We use measure theory (Lebesgue and Hausdorff measure) to generalize differential geometry to enable us to deal with maps and surface that are not necessarily smooth. We discuss the fundamental theorem of geometric measure theory (Compactness theorem) that guarantees solutions to a wide class of variational problems and soap bubble clusters.الرياضياتMathematical Statistics