A criterion for the unique determination of domains in Euclidean spaces by the metrics of their boundaries induced by the intrinsic metrics of the domains |
| |
Authors: | M V Korobkov |
| |
Institution: | 1.Sobolev Institute of Mathematics,Novosibirsk,Russia |
| |
Abstract: | We say that a domain U ⊂ ℝ
n
is uniquely determined by the relative metric (which is the extension by continuity of the intrinsic metric of the domain
on its boundary) of its Hausdorff boundary if any domain V ⊂ ℝ
n
such that its Hausdorff boundary is isometric in the relative metric to the Hausdorff boundary of U, is isometric to U in the Euclidean metric. In this paper, we obtain the necessary and sufficient conditions for the uniqueness of determination
of a domain by the relative metric of its Hausdorff boundary. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|