良好的阴影、动态和凸包
Good shadows, dynamics, and convex hulls
摘要：
Ekeland变分原理暗示了在$C^1$类别中可以被视为Yau最小值原理的强版本：在适当的假设下，{ \it every}最小化序列允许{ \it good shadow}，第二个最小化序列具有良好的性质并且渐进于原始序列。利用动力系统的参数，我们给出了这一结果的另一个证明，并建立了一个特殊的情况下，与格罗莫夫的体积比的单调性定理的帮助下，猜想声称存在良好的阴影在原来的$C^2$设置的丘最小值原理。对具有丰富的良好阴影的兴趣源于这样一个事实，即如果想要改进渐近最小值原理的应用，这是一个期望的性质，因为它允许信息被定位在无穷远处。本文将这些思想应用于研究欧氏$n$ -空间中控制Grassmanian值Gauss映射的完备子流形的凸包。
英文摘要：
The Ekeland variational principle implies what can be regarded as a strong version, in the $C^1$ category, of the Yau minimum principle: under the appropriate hypotheses {\it every} minimizing sequence admits a {\it good shadow}, a second minimizing sequence that has good properties and is asymptotic to the original one. Using arguments from dynamical systems, we give another proof of this result and also establish, with the aid of Gromov's theorem on monotonicity of volume ratios, a special case of a conjecture claiming the existence of good shadows in the original $C^2$ setting of the Yau minimum principle. The interest in having an abundance of good shadows stems from the fact that this is a desirable property if one wants to refine the applications of the asymptotic minimum principle, as it allows for information to be localized at infinity. These ideas are applied in this paper to the study of the convex hulls of complete submanifolds of Euclidean $n$-space that have controlled Grassmanian-valued Gauss maps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
