Related papers: Gradient estimates for mean curvature flow with Ne…
In this paper, we can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an $n$-dimensional…
We define a notion of mean curvature flow with surgery for two-dimensional surfaces in $\mathbb{R}^3$ with positive mean curvature. Our construction relies on the earlier work of Huisken and Sinestrari in the higher dimensional case. One of…
We study families of smooth immersed regular planar curves $ \alpha : \left [-1,1 \right ]\times \left [0,T \right )\to \mathbb{R}^{2}$ satisfying the fourth order nonlinear curve diffusion flow with generalised Neumann boundary conditions…
The evaluation and consideration of the mean flow in wave evolution equations are necessary for the accurate prediction of fluid particle trajectories under wave groups, with relevant implications in several domains, from the transport of…
The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$.…
We investigate the convergence of the mean curvature flow of arbitrary codimension in Riemannian manifolds with bounded geometry. We prove that if the initial submanifold satisfies a pinching condition, then along the mean curvature flow…
In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in $R^{n+1}$. We study the basic properties, such as positivity preserving property, of the…
We prove the Li-Yau gradient estimate for the heat kernel on graphs. The only assumption is a variant of the curvature-dimension inequality, which is purely local, and can be considered as a new notion of curvature for graphs. We compute…
We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of…
Given a singular Riemannian foliation on a compact Riemannian manifold, we study the mean curvature flow equation with a regular leaf as initial datum. We prove that if the leaves are compact and the mean curvature vector field is basic,…
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…
Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of P\'eclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these…
We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection.…
The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream…
We study the formation of generic singularities of mean curvature flow by combining the different approaches, specifically the methods in studying blowup of nonlinear heat equations, the techniques used by the author and the collaborators…
This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with…
In this Thesis, we study the behavior of spectral curves of quantum graphs under certain families of vertex conditions, called the $\delta_s$ family, which we define in this work. We focus on studying two main quantities related to the…
The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity,…
In this paper, we investigate the mean curvature flow having equifocal submanifolds as initial data. The investigation are performed by investigating the mean curvature flow having the lifted submanifolds to a Hilbert space through a…
We exploit a result by Nerman which shows that conditional limit theorems hold when a certain monotonicity condition is satisfied. Our main result is an application to vertex degrees in random graphs, where we obtain asymptotic normality…