Geometric Analysis is one of the most active research fields nowadays. The interplay between geometric and analytic techniques is at the core of recent remarkable advances in Differential Geometry and Topology. However, the majority of the monographs and books on the subject focus on intrinsic Riemannian Geometry techniques and applications. A systematic treatment of problems involving the extrinsic curvature of submanifolds is still missing in the literature. In particular, up to our knowledge, there are no references joining the geometric and analytic aspects of the theory of...