Stability and bifurcation for periodic minimal surfaces and surfaces with constant mean curvature, and applications to other fields

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We studied surfaces with constant mean curvature and surfaces with constant anisotropic mean curvature with free or fixed boundary. We obtained results about existence, uniqueness, geometric properties of solutions or stable solutions. Also, we obtained sufficient conditions for the existence of bifurcationand criterion of the stability for each surface in the bifurcation branch. Moreover,by removing the convexity assumption for the anisotropic surface energy, we studied uniformly a large class of surfaces including constant mean curvature surfaces in the Lorentz-Minkowski space and obtained a new uniqueness theorem and examples.