de Clercq, Adriaan2023-09-192023-09-192023-05https://hdl.handle.net/11299/256936University of Minnesota M.S. thesis. May 2023. Major: Mathematics. Advisor: Max Engelstein. 1 computer file (PDF); ii, 75 pages.We show the existence and regularity of the Cheeger cut on a closed Riemannian manifold. We show quantitative stability of the Cheeger cut for closed Riemannian manifolds of dimensions 2 ≤ n ≤ 7, and show that the stability estimate achieved is sharp. The main novelty of this work is in showing stability for a non-smooth functional.enThesis or Dissertation