4 papers
Möbius Maps, Reflections and Lipschitz Constants
Alan F. Beardon, Toshiyuki Sugawa, Matti Vuorinen
We introduce the chordal isometric circle of a Möbius map, and use this to give a factorization of any Möbius map as the composition of a chordal isometry and either a reflection,…
Modulus estimates and cavitation in higher dimensions
Anatoly Golberg, Vladimir Gutlyanskiĭ, Vladimir Ryazanov +1
We explore the phenomenon of cavitation in higher-dimensional elasticity, defining it as the mapping of a punctured ball onto a non-degenerate ring domain. Crucially, for the class…
Modulus estimates of semirings with applications to boundary extension problems
Anatoly Golberg, Toshiyuki Sugawa, Matti Vuorinen
In our previous paper [GSV2020], we proved that the complementary components of a ring domain in with large enough modulus may be separated by an annular ring domain…
Intrinsic geometry and boundary structure of plane domains
Oona Rainio, Toshiyuki Sugawa, Matti Vuorinen
For a non-empty compact set in a proper subdomain of the complex plane, we denote the diameter of and the distance from to the boundary of by and $d(E,\p…