Search results for "Simply connected at infinity"
showing 3 items of 3 documents
Radó-Kneser-Choquet Theorem for simply connected domains (p-harmonic setting)
2018
A remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically onto Q . Numerous extensions of this result for linear and nonlinear elliptic PDEs are known, but only when ⌦ is a Jordan domain or, if not, under additional assumptions on the boundary map. On the other hand, the newly developed theory of Sobolev mappings between Euclidean domains and Riemannian manifolds demands to extend this theorem to the setting on simply connected domains. This is the primary goal of our article. The class of the p -harmonic equations is wide enou…
On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form
1996
We give a nonimmersibility theorem of a compact manifold with nonnegative scalar curvature bounded from above into a geodesic ball of a simply connected space form.
The ends of manifolds with bounded geometry, linear growth and finite filling area
2002
We prove that simply connected open Riemannian manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.