Pinching estimates and motion of hypersurfaces by curvature functions
Pinching estimates and motion of hypersurfaces by curvature functions
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DOI：
10.1515/crelle.2007.051
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发表时间：
2004-02
期刊：
影响因子：
--
通讯作者：
B. Andrews
中科院分区：
文献类型：
--
作者：
B. Andrews
摘要 二阶导数箍缩估计被证明适用于一类抛物线方程，包括通过曲率函数（例如曲率初等对称函数的商）进行的超曲面运动。这些估计意味着在这些流动下凸超曲面会收敛到球体，从而改进了 B. Chow 和作者的早期结果。结果是通过对二阶导数满足的方程中的梯度项进行详细分析而获得的。
Abstract Second derivative pinching estimates are proved for a class of parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B. Chow and the author. The result is obtained via a detailed analysis of gradient terms in the equations satisfied by second derivatives.