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Full-Text Articles in Physical Sciences and Mathematics
Regularity Of Mean Curvature Flow Of Graphs On Lie Groups Free Up To Step 2, Luca Capogna, Giovanna Citti, Maria Manfredini
Regularity Of Mean Curvature Flow Of Graphs On Lie Groups Free Up To Step 2, Luca Capogna, Giovanna Citti, Maria Manfredini
Mathematics Sciences: Faculty Publications
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 parameter family of Riemannian metrics σ ε collapsing to a subRiemannian metric σ0 as ε → 0. We establish Ckα estimates for this flow, that are uniform as ε → 0 and as a consequence prove long time existence for the subRiemannian mean curvature flow of the graph. Our proof extend to the setting of every step two Carnot group (not necessarily free) and can be adapted following …
Uniform Gaussian Bounds For Subelliptic Heat Kernels And An Application To The Total Variation Flow Of Graphs Over Carnot Groups, Luca Capogna, Giovanna Citti, Maria Manfredini
Uniform Gaussian Bounds For Subelliptic Heat Kernels And An Application To The Total Variation Flow Of Graphs Over Carnot Groups, Luca Capogna, Giovanna Citti, Maria Manfredini
Mathematics Sciences: Faculty Publications
In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σϵ which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ϵ rarr; 0. The main new contribution are Gaussian-Type bounds on the heat kernel for the σϵ metrics which are stable as ϵ rarr; 0 and extend the previous time-independent estimates in [16]. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in a step two Carnot group (G; σϵ ). We establish …
Generalized Mean Curvature Flow In Carnot Groups, Luca Capogna, Giovanna Citti
Generalized Mean Curvature Flow In Carnot Groups, Luca Capogna, Giovanna Citti
Mathematics Sciences: Faculty Publications
In this paper we study the generalized mean curvature flow of sets in the sub-Riemannian geometry of Carnot groups. We extend to our context the level sets method and the weak (viscosity) solutions introduced in the Euclidean setting in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow.
A Note On The Engulfing Property And The R 1+Α -Regularity Of Convex Functions In Carnot Groups, Luca Capogna, Diego Maldonado
A Note On The Engulfing Property And The R 1+Α -Regularity Of Convex Functions In Carnot Groups, Luca Capogna, Diego Maldonado
Mathematics Sciences: Faculty Publications
We study the engulfing property for convex functions in Carnot groups. As an application we show that the horizontal gradient of functions with this property is Hölder continuous.