论文标题
非均匀曲率流的收缩自相似解决方案
Contracting self-similar solutions of nonhomogeneous curvature flows
论文作者
论文摘要
Li and LV最近的一篇文章考虑了曲面的某些非均匀函数对凸超曲面的完全非线性收缩，在有限时间的情况下，在有限时间的速度中，在速度是一种程度的同质，凹面，凹面和反倒置的情况下，在有限时间内收敛。在本文中，我们考虑了对这些和相关的曲率流的自相似解决方案，这些解决方案在原理曲率上不是同质的，发现各种情况，这些情况封闭，凸出弯曲的弯曲性超丘脑自我相似。
A recent article by Li and Lv considered fully nonlinear contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in cases where the speed is a function of a degree-one homogeneous, concave and inverse concave function of the principle curvatures. In this article we consider self-similar solutions to these and related curvature flows that are not homogeneous in the principle curvatures, finding various situations where closed, convex curvature-pinched hypersurfaces contracting self-similarly are necessarily spheres.
