Geometric measure theory and minimal surfaces

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The proposed research is in geometric measure theory. The primary focus is the study of minimal surfaces, minimal sets, and varifolds, attempting the solution of various open problems in the area. The secondary focus is the study of (Besicovitch type) covering theorems in doubling metric spaces.The direct beneficiaries are mathematicians with interests in geometric measure theory or analysis in metric spaces and nearby fields.This research fits into EPSRC's Mathematical analysis research area.