A class of one-dimensional geometric variational problems with energy involving the curvature and its derivatives: some results aimed to a geometric measure-theoretic approach

摘要

The notions of Legendrian and Gaussian towers are defined and indagated. Then applications in the context of one-dimensional geometric variational problems with the energy involving the curvature and its derivatives are provided. Particular attention is paid to the case when the functional is defined on smooth boundaries of plane sets.