Curve Shortening Flow in a Riemannian Manifold
| dc.creator | Ma, Li | |
| dc.creator | Chen, Dezhong | |
| dc.date | 2003-12-26 | |
| dc.date.accessioned | 2026-07-07T05:04:12Z | |
| dc.date.available | 2026-07-07T05:04:12Z | |
| dc.description | In this paper, we systemally study the long time behavior of the curve shortening flow in a closed or non-compact complete locally Riemannian symmetric manifold. Assume that we have a global flow. Then we can exhibit a a limit for the global behavior of the flow. In particular, we show the following results. 1). Let $\mathbf{M}$ be a compact locally symmetric space. If the curve shortening flow exists for infinite time, and $$ \lim_{t\to\infty}L(γ_{t})>0, $$ then for every $n>0$, $$ \lim_{t\to \infty}\sup(|\frac{D^{n}T}{\partial s^{n}}|)=0. $$ In particular, the limiting curve exists and is a closed geodesic in $\mathbf{M}$. 2). For $γ_{0}$ is a ramp, we have a global flow and the flow converges to a geodesic in $C^{\infty}$ norm. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312463 | |
| dc.identifier | http://arxiv.org/abs/math/0312463 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69713 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C44 | |
| dc.title | Curve Shortening Flow in a Riemannian Manifold | |
| dc.type | text |