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articleNo Access
Slowly converging Yamabe-type flow on manifolds with boundary
- Pak Tung Ho and
- Jinwoo Shin
Communications in Contemporary Mathematics13 Dec 2022
Preview Abstract
Carlotto, Chodosh and Rubinstein studied the rate of convergence of the Yamabe flow on a closed (compact without boundary) manifold $M$ :
$\frac{\partial}{\partial t} g (t) = - (R_{g (t)} - {\bar{R}}_{g (t)}) g (t) in M .$
In this paper, we prove the corresponding results on manifolds with boundary. More precisely, given a compact manifold $M$ with smooth boundary $\partial M$ , we study the convergence rate of the Yamabe flow with boundary:
$\frac{\partial}{\partial t} g (t) = - (R_{g (t)} - {\bar{R}}_{g (t)}) g (t) in M and H_{g (t)} = 0 on \partial M$
and the conformal mean curvature flow:
$\frac{\partial}{\partial t} g (t) = - (H_{g (t)} - {\bar{H}}_{g (t)}) g (t) on \partial M and R_{g (t)} = 0 in M .$

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