UC Berkeley

Let (M,g) be a Riemannian manifold of dimension greater or equal to 3, and let Sigma in M be

an immersed hypersurface with prescribed mean curvature. I study the geometry of Euler-Lagrange equations in this particular context. This includes a characterization of those prescribed mean curvature systems that are Euler-Lagrange, and I prove that these are locally conformally equivalent to basic systems. Finally, I study Emmy Noether's theorem for first-order conservation laws in the special case of minimal surfaces in Riemannian 3-manifolds. In particular, I am able to identify which conservation laws do arise from symmetries of the system in the sense of Noether and which ones do not.