Browsing by Subject "Mean curvature"
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Item Stability and behavior of critical points in the capillarity droplet problem(2018-05-01) Mihaila, Cornelia; Maggi, Francesco, 1978-; Caffarelli, Luis; Figalli, Alessio; Patrizi, Stefania; Vasseur, AlexisIn this thesis we characterize minimizers, critical points, and almost-critical points in the capillarity droplet problem. We first develop a qualitative description of global minimizers for the classic problem describing a droplet of liquid in a container. We then prove a compactness theorem for volume-constrained almost-critical points of elliptic integrands. As applications of this theorem we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential and we prove an Aleksandrov-type theorem for crystalline isoperimetric problems. Lastly we develop a nonlocal analogue for the classical result of Wente, which demonstrates the axial symmetry of sessile droplets.