Mathematical Sciences: RUI: Quasisymmetric Embeddings

在这个项目中，首席研究员将研究 拟对称嵌入和相关的映射类。 在 特别是，她将着眼于p维欧几里德映射 空间到n维空间，其中p在1和n-1之间。 一 研究的主要目的是将所有这些 嵌入的准对称常数等于1。 目前在这个方向上的结果是已知的情况p=n p=1，n=2。 可以预期，对于p=n-1的情况， 这种嵌入是仿射（线性+常数）嵌入。 复变量的大部分内容都与 所谓的“几何函数理论”，其中的子区域， 人们研究函数或映射的性质， 函数定义域的几何形状（上的点集 函数的定义）和函数的范围（ 函数的值）。 在这个项目中，校长 研究人员将研究某些类型的映射， 不同维度的欧几里得空间， 以规定的方式。 这项研究的目的是将所有 具有给定失真的函数类型。

In this project the principal investigator will study quasisymmetric embeddings and related classes of mappings. In particular, she will look at mappings of p-dimensional euclidean space into n-dimensional space, where p is between 1 and n-1. A major objective of the research is to classify all such embeddings that have a quasisymmetry constant equal to one. Currently results in this direction are known for the cases p=n and p=1, n=2. It is expected that for the case p=n-1 the only such embeddings are affine (linear + constant) embeddings. Much of the subject of complex variables is concerned with what is called "geometric function theory", the subarea in which one studies the properties of functions or mappings in terms of the geometry of the domain of the function (the set of points on which the function is defined) and the range of the function (the set of values of the function). In this project the principal investigator will study certain types of mappings between euclidean spaces of different dimensions that distort the spaces in a prescribed way. The goal of the research is to classify all types of functions that have a given distortion.