Speaker
Monica Musso, University of Bath
Abstract
This course explores a variational problem arising from the liquid drop model, which balances perimeter minimization with long-range interactions. We study equilibrium shapes of regions that minimize an energy functional involving surface area and Coulomb interaction, focusing on the interplay between these competing effects. A key aspect is the connection to constant mean curvature (CMC) surfaces, including spheres, Delaunay unduloids, and novel equilibrium configurations. We will analyze existence, stability, and bifurcation phenomena in this setting, using tools from geometric analysis, PDEs, and calculus of variations.
Monica Musso, University of Bath
Abstract
This course explores a variational problem arising from the liquid drop model, which balances perimeter minimization with long-range interactions. We study equilibrium shapes of regions that minimize an energy functional involving surface area and Coulomb interaction, focusing on the interplay between these competing effects. A key aspect is the connection to constant mean curvature (CMC) surfaces, including spheres, Delaunay unduloids, and novel equilibrium configurations. We will analyze existence, stability, and bifurcation phenomena in this setting, using tools from geometric analysis, PDEs, and calculus of variations.