Sub-Riemannian mean curvature flow for image processing
In this paper we reconsider the sub-Riemannian cortical model of image completion
introduced in [G. Citti and A. Sarti, J. Math. Imaging Vision, 24 (2006), pp. 307--326]. This …
introduced in [G. Citti and A. Sarti, J. Math. Imaging Vision, 24 (2006), pp. 307--326]. This …
Regularity for subelliptic PDE through uniform estimates in multi-scale geometries
We aim at reviewing and extending a number of recent results addressing stability of certain
geometric and analytic estimates in the Riemannian approximation of subRiemannian …
geometric and analytic estimates in the Riemannian approximation of subRiemannian …
On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group
F Ferrari, Q Liu, JJ Manfredi - Communications in Contemporary …, 2014 - World Scientific
We study the horizontal mean curvature flow in the Heisenberg group by using the level-set
method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions …
method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions …
A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow
This paper is concerned with a PDE approach to horizontally quasiconvex (h-quasiconvex)
functions in the Heisenberg group based on a nonlinear second order elliptic operator. We …
functions in the Heisenberg group based on a nonlinear second order elliptic operator. We …
Sub-Riemannian heat kernels and mean curvature flow of graphs
We introduce a sub-Riemannian analogue of the Bence–Merriman–Osher algorithm
(Merriman et al., 1992 [42]) and show that it leads to weak solutions of the horizontal mean …
(Merriman et al., 1992 [42]) and show that it leads to weak solutions of the horizontal mean …
Global weak solutions for the inverse mean curvature flow in the Heisenberg group
A Pisante, E Vecchi - arXiv preprint arXiv:2406.15123, 2024 - arxiv.org
We consider the inverse mean curvature flow (IMCF) in the Heisenberg group $(\He^ n,
d_\varepsilon) $, where $ d_\varepsilon $ is distance associated to either $|\cdot …
d_\varepsilon) $, where $ d_\varepsilon $ is distance associated to either $|\cdot …
Minimal surfaces in sub-Riemannian structures and functional geometry of the visual cortex
E Baspinar - 2018 - amsdottorato.unibo.it
We develop geometrical models of vision consistent with the characteristics of the visual
cortex and study geometric flows in the relevant model geometries. We provide a novel sub …
cortex and study geometric flows in the relevant model geometries. We provide a novel sub …
Regularity of mean curvature flow of graphs on Lie groups free up to step 2
We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains
in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one …
in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one …
Horizontal mean curvature flow as a scaling limit of a mean field equation in the Heisenberg group
G Citti, N Dirr, F Dragoni, R Grande - arXiv preprint arXiv:2411.15814, 2024 - arxiv.org
We derive curvature flows in the Heisenberg group by formal asymptotic expansion of a
nonlocal mean-field equation under the anisotropic rescaling of the Heisenberg group. This …
nonlocal mean-field equation under the anisotropic rescaling of the Heisenberg group. This …
Uniqueness of viscosity mean curvature flow solution in two sub-Riemannian structures
E Baspinar, G Citti - SIAM Journal on Mathematical Analysis, 2019 - SIAM
We provide a uniqueness result for a class of viscosity solutions to sub-Riemannian mean
curvature flows. In a sub-Riemannian setting, uniqueness cannot be deduced by the …
curvature flows. In a sub-Riemannian setting, uniqueness cannot be deduced by the …