8 papers
Warped product spaces: Gromov hyperbolicity and identification of the visual boundary
Josh Kline, Nageswari Shanmugalingam, Gareth Speight +1
In this paper, we consider warped product spaces , where is a complete geodesic Gromov hyperbolic space, is a compact geodesic metric space, and the warping fu…
Geometric inequalities related to fractional perimeter: fractional Poincaré, isoperimetric, and boxing inequalities in metric measure spaces
Josh Kline, Panu Lahti, Jiang Li +1
In the setting of a complete, doubling metric measure space supporting a -Poincaré inequality, we show that for all , the following fractional Poincaré…
Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces
Iván Caamaño, Josh Kline
In the setting of a non-complete doubling metric measure space , we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Beso…
Warped products, solid hyperbolic fillings, and the identity
Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam +1
We construct a large class of metric measure spaces which satisfy the identity , i.e.\ any measurable function …
Large-scale behaviour of Sobolev functions in Ahlfors regular metric measure spaces
Josh Kline, Pekka Koskela, Khanh Nguyen
In this paper, we study the behaviour at infinity of -Sobolev functions in the setting of Ahlfors -regular metric measure spaces supporting a -Poincaré inequality. By int…
Well-posedness of Dirichlet boundary value problems for reflected fractional -Laplace-type inhomogeneous equations in compact doubling metric measure spaces
Josh Kline, Feng Li, Nageswari Shanmugalingam
In this paper we consider the setting of a locally compact, non-complete metric measure space equipped with a doubling measure , under the condition that the boundar…