A Remark on Soliton Equation of Mean Curvature Flow
| dc.creator | Ma, L. | |
| dc.creator | Yang, Y. | |
| dc.date | 2003-12-08 | |
| dc.date.accessioned | 2026-07-07T05:03:38Z | |
| dc.date.available | 2026-07-07T05:03:38Z | |
| dc.description | In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension. We show that the following is true: Let $F(x) = (x,f(x)), x \in \mathbb{R}^{n}$ be a graph solution to the soliton equation $$ \bar{H}(x) + F^{\bot}(x) = 0. $$ Assume $\sup_{\mathbb{R}^{n}}|Df(x)| \le C_{0} < + \infty$. Then there exists a unique smooth function $f_{\infty}: \mathbb{R}^{n}\to \mathbb{R}^k$ such that $$ f_{\infty}(x) = \lim_{λ\to \infty}f_λ(x) $$ and $$ f_{\infty}(r x)=r f_{\infty}(x) $$ for any real number $r\not= 0$, where $$ f_λ(x) = λ^{-1}f(λx). $$ | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312151 | |
| dc.identifier | http://arxiv.org/abs/math/0312151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69503 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C44,53C42 | |
| dc.title | A Remark on Soliton Equation of Mean Curvature Flow | |
| dc.type | text |