本项目拟研究高维Frobenius问题及其在自相似集的Lipschitz等价上的应用。 一维Frobenius问题是一个经典的数论问题，我们在前期工作[17,18]中引入了高维Frobenius问题，在共面条件下研究了其方向增长函数和刚性，并把这些结果应用于自相似集的Lipschitz等价。. 本项目拟继续研究不共面情形下的高维Frobenius问题，包括极大锥的顶点估计，重数估计及应用，方向增长函数和线性约束条件熵的关系以及刚性问题。我们将把这些研究应用于不共面情形的Lipschitz等价的Falconer-Marsh问题。. 此外，本项目也计划在比较简单的情形下，研究自仿集的Lipschitz等价问题。

This research intends to study higher dimensional Frobenius problem and applies this results to the study of Lipschitz equivalence of self-similar sets. One-dimensional Frobenius problem is a classical problem of Number Theory. In our works[17,18], we introduced higher dimensional Frobenius problem, and studied its directional growth function and rigidity under coplanar condition, and applied this results to the study of Lipschitz equivalence of self-similar sets.. We will continue to investigate higher dimensional Frobenius problem under non-coplanar condition. We will estimate the vertices of maximal saturated cone and multiplicity function and its application. We will study the relation between directional growth function and maximal entropy under linear constraints, and study the rigidity. This results will be applied to the study of Lipschitz equivalence of self-similar sets under non-coplanar condition.. In addition, we also plan to study the Lipschitz equivalence of a simple class of planar self-affine sets.