Related papers: Median filter method for mean curvature flow using…
This paper proves error estimates for $H^2$ conforming finite elements for equations which model the flow of surfaces by different powers of the mean curvature (this includes mean curvature flow). for an adapted scheme originally proposed…
We present a robust and efficient numerical framework based on a median filter scheme for solving a broad class of interface-related optimization problems, from image segmentation to topology optimization. A key innovation of our work is…
We construct smooth mean curvature flows with surgery that approximate weak mean curvature flows with only spherical and neck-pinch singularities. This is achieved by combining the recent work of Choi-Haslhofer-Hershkovits, and…
We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…
We propose a construction of mean curvature flows by approximation for very general initial data, in the spirit of the works of Brakke and of Kim & Tonegawa based on the theory of varifolds. Given a general varifold, we construct by…
We prove two new estimates for the level set flow of mean convex domains in Riemannian manifolds. Our estimates give control - exponential in time - for the infimum of the mean curvature, and the ratio between the norm of the second…
We provide a probabilistic proof of a well known connection between a special case of the Allen-Cahn equation and mean curvature flow. We then prove a corresponding result for scaling limits of the spatial $\Lambda$-Fleming-Viot process…
We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive anisotropic mean curvature. We show that such condition is preserved by the scheme, and we prove the strict…
Normalizing flows learn a diffeomorphic mapping between the target and base distribution, while the Jacobian determinant of that mapping forms another real-valued function. In this paper, we show that the Jacobian determinant mapping is…
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We…
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…
This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in…
In this paper, we consider the filtering problem for partially observed diffusions, which are regularly observed at discrete times. We are concerned with the case when one must resort to time-discretization of the diffusion process if the…
In this paper, using heat kernel estimates and contraction mapping principle, we give a new proof of the existence and uniqueness of mean curvature flow starting from hypersurface with bounded second fundamental form. Moreover, we show the…
The Merriman-Bence-Osher (MBO) scheme, also known as thresholding or diffusion generated motion, is an efficient numerical algorithm for computing mean curvature flow (MCF). It is fairly well understood in the case of hypersurfaces. This…
We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for…
We show that a generic levelset of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…
The hyperbolic MBO is a threshold dynamic algorithm which approximates interfacial motion by hyperbolic mean curvature flow. We introduce a generalization of this algorithm for imparting damping terms onto the equation of motion. We also…