44 citations · 58 across the 11 of their papers we have counts for
15 papers
A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group
A. Cesaroni, M. Novaga, P. Pozzi
The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement sch…
On an elastic flow for parametrized curves in suitable for numerical purposes
Paola Pozzi
In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in was introduced, that is more suitable for numerical purposes. Here we investigate…
Convergence of a scheme for elastic flow with tangential mesh movement
Paola Pozzi, Björn Stinner
Elastic flow for closed curves can involve significant deformations. Mesh-based approximation schemes require tangentially redistributing vertices for long-time computations. We pr…
Anisotropic curvature flow of immersed networks
Heiko Kroener, Matteo Novaga, Paola Pozzi
We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, unique…
Elastic flow of networks: short-time existence result
Anna Dall'Acqua, Chun-Chi Lin, Paola Pozzi
In this paper we study the -gradient flow of the penalized elastic energy on networks of -curves in for . Each curve is fixed at one end-point and at the…
A converging finite element scheme for motion by curvature of a network with a triple junction
Paola Pozzi, Björn Stinner
A new semi-discrete finite element scheme for the evolution of three parametrized curves by curvature flow that are connected by a triple junction is presented and analyzed. In thi…
A second order gradient flow of p-elastic planar networks
Matteo Novaga, Paola Pozzi
We consider a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths. We construct a weak solution of the flow by means of…
Flow of elastic networks: long-time existence result
Anna Dall'Acqua, Chun-Chi Lin, Paola Pozzi
We provide a long-time existence and sub-convergence result for the elastic flow of a three network in under some mild topological assumptions. The evolution is su…
A gradient flow for the p-elastic energy defined on closed planar curves
Shinya Okabe, Paola Pozzi, Glen Wheeler
We study the evolution of closed inextensible planar curves under a second order flow that decreases the -elastic energy. A short time existence result for is…
Elastic flow interacting with a lateral diffusion process: The one-dimensional graph case
Paola Pozzi, Björn Stinner
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated an…
Anisotropic curvature flow of immersed curves
Gwenael Mercier, Matteo Novaga, Paola Pozzi
We prove short-time existence of ϕ-regular solutions to the anisotropic and crystalline curvature flow of immersed planar curves.
The Łojasiewicz-Simon gradient inequality for open elastic curves
Anna Dall'Acqua, Paola Pozzi, Adrian Spener
In this paper we consider the elastic energy for open curves in Euclidean space subject to clamped boundary conditions and obtain the Łojasiewicz-Simon gradient inequality for this…
Curve shortening flow coupled to lateral diffusion
Paola Pozzi, Bjorn Stinner
We present and analyze a semi-discrete finite element scheme for a system consisting of a geometric evolution equation for a curve and a parabolic equation on the evolving curve. M…
A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow
Ricardo Perl, Paola Pozzi, Martin Rumpf
A variational time discretization of anisotropic Willmore flow combined with a spatial discretization via piecewise affine finite elements is presented. Here, both the energy and t…
Willmore-Helfrich L^{2}-flow of curves with natural boundary conditions
Anna Dall'Acqua, Paola Pozzi
We consider regular open curves in R^n with fixed boundary points and moving according to the L^{2}-gradient flow for a generalisation of the Helfrich functional. Natural boundary…