Josh Kline

activity

20232026

collaborators

9 papers

math.MG2026

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 $X \times_{φ} Y$ , where $X$ is a complete geodesic Gromov hyperbolic space, $Y$ is a compact geodesic metric space, and the warping fun…

math.FA2025

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 $(X, d, μ)$ supporting a $(1, 1)$ -Poincaré inequality, we show that for all $0 < θ < 1$ , the following fractional Poincaré ineq…

math.MG2025

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 $(Ω, d, μ)$ , we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov…

math.MG2025

Warped products, solid hyperbolic fillings, and the identity $D^{1, p} = N^{1, p} + R$

Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam +1

We construct a large class of metric measure spaces $Z$ which satisfy the identity $D^{1, p} (Z) = N^{1, p} (Z) + R$ , i.e.\ any measurable function $u : Z \to R$ …

math.AP2024

Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings

Sylvester Eriksson-Bique, Josh Kline

In this paper, we prove a self-improvement result for $(θ, p)$ -fractional Hardy inequalities, in both the exponent $1 < p < \infty$ and the regularity parameter $0 < θ < 1$ , for bounded dom…

math.AP2024

Well-posedness of Dirichlet boundary value problems for reflected fractional $p$ -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 $(Z, d, ν)$ equipped with a doubling measure $ν$ , under the condition that the boundary…

math.AP2024

Regularity of sets of finite fractional perimeter and nonlocal minimal surfaces in metric measure spaces

Josh Kline

In the setting of a doubling metric measure space, we study regularity of sets with finite $s$ -perimeter, that is, sets whose characteristic functions have finite Besov energy, wit…

math.CA2023

Characterization of the upper Assouad codimension

Josh Kline, Antti V. Vähäkangas

We present a new notion, the upper Aikawa codimension, and establish its equivalence with the upper Assouad codimension in a metric space with a doubling measure. To achieve this r…

math.FA2023

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 $p$ -Sobolev functions in the setting of Ahlfors $Q$ -regular metric measure spaces supporting a $p$ -Poincaré inequality. By intr…

Warped product spaces: Gromov hyperbolicity and identification of the visual boundary

Geometric inequalities related to fractional perimeter: fractional Poincaré, isoperimetric, and boxing inequalities in metric measure spaces

Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces

Warped products, solid hyperbolic fillings, and the identity D1,p=N1,p+R

Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings

Well-posedness of Dirichlet boundary value problems for reflected fractional p-Laplace-type inhomogeneous equations in compact doubling metric measure spaces

Regularity of sets of finite fractional perimeter and nonlocal minimal surfaces in metric measure spaces

Characterization of the upper Assouad codimension

Large-scale behaviour of Sobolev functions in Ahlfors regular metric measure spaces

Warped products, solid hyperbolic fillings, and the identity $D^{1, p} = N^{1, p} + R$

Well-posedness of Dirichlet boundary value problems for reflected fractional $p$ -Laplace-type inhomogeneous equations in compact doubling metric measure spaces