1,127 research outputs found
The theory of prime ends and spatial mappings
It is given a canonical representation of prime ends in regular spatial
domains and, on this basis, it is studied the boundary behavior of the
so-called lower Q-homeomorphisms that are the natural generalization of the
quasiconformal mappings. In particular, it is found a series of effective
conditions on the function Q(x) for a homeomorphic extension of the given
mappings to the boundary by prime ends in domains with regular boundaries. The
developed theory is applied, in particular, to mappings of the classes of
Sobolev and Orlicz-Sobolev and also to finitely bi-Lipschitz mappings that a
far-reaching extension of the well--known classes of isometric and
quasiisometric mappings.Comment: 40 pages, we improve modulus estimates and on this basis prove a
series of new criteria for homeomorphic extension of spatial mappings to the
boundary by prime ends in terms of inner dilatation
Orientation and symmetries of Alexandrov spaces with applications in positive curvature
We develop two new tools for use in Alexandrov geometry: a theory of ramified
orientable double covers and a particularly useful version of the Slice Theorem
for actions of compact Lie groups. These tools are applied to the
classification of compact, positively curved Alexandrov spaces with maximal
symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice
Theorem, correcting omissions in the previous versio
- …