34 citations · 112 across the 12 of their papers we have counts for
14 papers
Fine properties of nonlinear potentials and a unified perspective on monotonicity formulas
Luca Benatti, Alessandra Pluda, Marco Pozzetta
We rigorously show that a large family of monotone quantities along the weak inverse mean curvature flow is the limit case of the corresponding ones along the level sets of -cap…
Minimizing properties of networks via global and local calibrations
Alessandra Pluda, Marco Pozzetta
In this note we prove that minimal networks enjoy minimizing properties for the length functional. A minimal network is, roughly speaking, a subset of composed of st…
On the uniqueness of nondegenerate blowups for the motion by curvature of networks
Alessandra Pluda, Marco Pozzetta
In this note we prove uniqueness of nondegenerate compact blowups for the motion by curvature of planar networks. The proof follows ideas introduced in "Lojasiewicz-Simon inequalit…
Łojasiewicz-Simon inequalities for minimal networks: stability and convergence
Alessandra Pluda, Marco Pozzetta
We investigate stability properties of the motion by curvature of planar networks. We prove Lojasiewicz-Simon gradient inequalities for the length functional of planar networks wit…
Asymptotic convergence of evolving hypersurfaces
Carlo Mantegazza, Marco Pozzetta
If is a smooth immersed closed hypersurface, we consider the functional , where is a local unit…
A survey of the elastic flow of curves and networks
Carlo Mantegazza, Alessandra Pluda, Marco Pozzetta
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In partic…
The Lojasiewicz-Simon inequality for the elastic flow
Carlo Mantegazza, Marco Pozzetta
We define the elastic energy of smooth immersed closed curves in as the sum of the length and the -norm of the curvature, with respect to the length measure. We…
Convergence of elastic flows of curves into manifolds
Marco Pozzetta
For a given , we define the -elastic energy of a closed curve immersed in a complete Riemannian manifold as the sum…
Connected surfaces with boundary minimizing the Willmore energy
Matteo Novaga, Marco Pozzetta
For a given family of smooth closed curves we consider the problem of finding an elastic \emph{connected} compact surface with boundary $γ=γ^1\…
Degenerate elastic networks
Giacomo Del Nin, Alessandra Pluda, Marco Pozzetta
We minimize a linear combination of the Willmore and the length functional among networks in belonging to a given class determined by the number of curves, the order…
Connected perimeter of planar sets
François Dayrens, Simon Masnou, Matteo Novaga +1
We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically conne…
A varifold perspective on the -elastic energy of planar sets
Marco Pozzetta
Under suitable regularity assumptions the -elastic energy of a planar set is defined to be …
On the Plateau-Douglas problem for the Willmore energy of surfaces with planar boundary curves
Marco Pozzetta
For a smooth closed embedded planar curve , we consider the minimization problem of the Willmore energy among immersed surfaces of a given genus having the c…
Confined Willmore energy and the Area functional
Marco Pozzetta
We consider minimization problems of functionals given by the difference between the Willmore functional of a closed surface and its area, when the latter is multiplied by a positi…