月曜解析セミナー： Homeomorphisms with integrally restricted \(p\)-moduli

開催日時

2017年2月5日 15時00分 ～ 2017年2月5日 16時30分

場所

理学部3号館210

講演者

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.