## 月曜解析セミナー： Homeomorphisms with integrally restricted $p$-moduli

2017年 　 2月 5日 15時 00分 ～ 2017年 　 2月 5日 16時 30分

Anatoly Golberg (Holon Institute of Technology, Israel)

We consider classes of homeomorphisms of domains in $\mathbb R^n$ with integrally bounded from above or below $p$-moduli of the families of curves and surfaces. Such mappings essentially extend the well-known customarily investigated classes of mappings such as quasiconformal, quaiisometric, Lipschitzian, etc. In contrast to these known classes, our generalized classes can be defined without any analytic restrictions. However, various differential properties of mappings can be derived on the base of estimates for $p$-moduli ($p$-capacities of condensers).

In the talk we survey the known results in this field, regarding mainly the regularity features of such mappings. A collection of open related problems will be also presented.