Existence of self-shrinkers to the degree-one curvature flow with a rotationally symmetric conical end
| Autor: | Guo, Siao-Hao |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a smooth, symmetric, homogeneous of degree one function $f\left(\lambda_{1},\cdots,\,\lambda_{n}\right)$ satisfying $\partial_{i}f>0$ for all $i=1,\cdots,\,n$, and a rotationally symmetric cone $\mathcal{C}$ in $\mathbb{R}^{n+1}$, we show that there is a $f$ self-shrinker (i.e. a hypersurface $\Sigma$ in $\mathbb{R}^{n+1}$ which satisfies $f\left(\kappa_{1},\cdots,\,\kappa_{n}\right)+\frac{1}{2}X\cdot N=0$, where $X$ is the position vector, $N$ is the unit normal vector, and $\kappa_{1},\cdots,\,\kappa_{n}$ are principal curvatures of $\Sigma$) that is asymptotic to $\mathcal{C}$ at infinity. Comment: arXiv:1604.08577v1 was split into arXiv:1604.08577v2 and this paper; published in Journal of Differential Equations |
| Databáze: | arXiv |
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