Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConvergence rate of the prescribed curvature flow
95
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The prescribed scalar curvature flow was introduced to study the problem of prescribing scalar curvature on manifolds. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the prescribed scalar curvature flow.
rate research
Read More
Assuming that there exists a translating soliton $u_infty$ with speed $C$ and prescribed contact angle, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to $u_infty +Ct$ as $ttoinfty$.
We prove an existence result for helicoidal graphs with prescribed mean curvature in a large class of warped product spaces which comprises space forms.
We consider a curvature flow $V=H$ in the band domain $Omega :=[-1,1]times R$, where, for a graphic curve $Gamma_t$, $V$ denotes its normal velocity and $H$ denotes its curvature. If $Gamma_t$ contacts the two boundaries $partial_pm Omega$ of $Omega$ with constant slopes, in 1993, Altschular and Wu cite{AW1} proved that $Gamma_t$ converges to a {it grim reaper} contacting $partial_pm Omega$ with the same prescribed slopes. In this paper we consider the case where $Gamma_t$ contacts $partial_pm Omega$ with slopes equaling to $pm 1$ times of its height. When the curve moves to infinity, the global gradient estimate is impossible due to the unbounded boundary slopes. We first consider a special symmetric curve and derive its uniform interior gradient estimates by using the zero number argument, and then use these estimates to present uniform interior gradient estimates for general non-symmetric curves, which lead to the convergence of the curve in $C^{2,1}_{loc} ((-1,1)times R)$ topology to the {it grim reaper} with span $(-1,1)$.
We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds $N$. More precisely, given a suitable subset $L$ of the asymptotic boundary of $N$ and a suitable function $H$ on $N$, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature $H$ provided that $N$ satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.
In this paper we investigate the singularities of Lagrangian mean curvature flows in $mathbf{C}^m$ by means of smooth singularity models. Type I singularities can only occur at certain times determined by invariants in the cohomology of the initial data. In the type II case, these smooth singularity models are asymptotic to special Lagrangian cones; hence all type II singularities are modeled by unions of special Lagrangian cones.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
