Meaning of horodisk | Babel Free

Definitions

A horocyclic disk

Examples

“In this paper we study⟳ the geometry and the topology of unbounded domains in the Hyperbolic Space #92;mathbb#123;H#125;ⁿ supporting a bounded positive solution to an overdetermined elliptic problem. Under suitable conditions on the elliptic problem and the behaviour of the bounded solution at infinity, we are able to show⟳ that symmetries of the boundary at infinity imply symmetries on the domain itself. In dimension two, we can strengthen our results proving that a connected domain #92;Omega#92;subset#92;mathbb#123;H#125;² with C² boundary whose complement is connected and supports a bounded positive solution u to an overdetermined problem, assuming natural conditions on the equation and the behaviour at infinity of the solution, must be either a geodesic ball or, a horodisk or, a half-space determined by a complete⟳ equidistant curve or, the complement of any of the above example.”

CEFR level