当前位置: X-MOL 学术J. Funct. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Flowing the leaves of a foliation with normal speed given by the logarithm of general curvature functions
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-04-22 , DOI: 10.1016/j.jfa.2021.109060
Heiko Kröner

Generalizing results of Chou and Wang [12] we study the flows of the leaves (MΘ)Θ>0 of a foliation of Rn+1{0} consisting of uniformly convex hypersurfaces in the direction of their outer normals with speeds log(F/f). For quite general functions F of the principal curvatures of the flow hypersurfaces and f a smooth and positive function on Sn (considered as a function of the normal) we show that there is a distinct leaf MΘ in this foliation with the property that the flow starting from MΘ converges to a translating solution of the flow equation. When starting the flow from a leave inside MΘ it shrinks to a point and when starting the flow from a leave outside MΘ it expands to infinity. While [12] considered this mechanism with F equal to the Gauss curvature we allow F to be among others the elementary symmetric polynomials Hk. Furthermore, we show that such kind of behavior is robust with respect to relaxing certain assumptions at least in the rotationally symmetric and homogeneous degree one curvature function case.



中文翻译:

由一般曲率函数的对数给出的以正常速度使叶的叶子流动

概括Chou和Wang [12]的结果,我们研究了叶子的流动 中号ΘΘ>0 叶的 [Rñ+1个{0} 由均匀的凸超曲面在其外法线方向上以速度组成 -日志F/F。对于一般函数,流动超曲面的主曲率Ff上的光滑正函数小号ñ (作为法线的函数),我们表明有一个明显的叶子 中号Θ 在这种叶状结构中,流动从 中号Θ收敛到流量方程的平移解。从内部离开开始流动时中号Θ 它缩小到一个点,当从外面的休假开始流动时 中号Θ它扩展到无穷大。尽管[12]认为这种机制的F等于高斯曲率,但我们允许F成为基本对称多项式等Hķ。此外,我们表明,这种行为至少在旋转对称且同质度一个曲率函数的情况下相对于放宽某些假设是鲁棒的。

更新日期:2021-04-29
down
wechat
bug