论文标题
波纹过程和$ε$ -ISOMPIT地图
Corrugation Process and $ε$-isometric maps
论文作者
论文摘要
凸集成是M. Gromov在70年代开发的一种理论。该理论允许解决满足某些凸假设的不同问题的家庭。从订阅中，该理论通过应用一系列凸集成来迭代地构建解决方案。在先前的论文ARXIV：1909.04908中，我们提议将通常的凸集成公式替换为一个称为波纹过程的新凸集成公式。当所考虑的差异问题具有Kuiper的特性时，这种新公式特别感兴趣。在本文中，我们考虑了$ε$ - 等级图的差异问题，并证明它是Codimension 1中的Kuiper。作为一个应用程序，我们构造了来自带有圆锥形奇异性的短地图的$ε$ - iSmotem-ismotem-imotem-imotem-imotemat图。
Convex Integration is a theory developed in the '70s by M. Gromov. This theory allows to solve families of differential problems satisfying some convex assumptions. From a subsolution, the theory iteratively builds a solution by applying a series of convex integrations. In a previous paper arXiv:1909.04908, we proposed to replace the usual convex integration formula by a new one called Corrugation Process. This new formula is of particular interest when the differential problem under consideration has the property of being of Kuiper. In this paper, we consider the differential problem of $ε$-isometric maps and we prove that it is Kuiper in codimension 1. As an application, we construct $ε$-isometric maps from a short map having a conical singularity.
