Josh Kline's Webpage

Preprints

Josh Kline, Panu Lahti, Jiang Li, Xiaodan Zhou. Geometric inequalities related to fractional perimeter: fractional Poincaré, isoperimetric, and boxing inequalities in metric measure spaces. Preprint (2025) (link to the arXiv version).
Ivan Caamano, Josh Kline. Trace and extension theorems for Besov functions in doubling metric measure spaces. Preprint (2025) (link to the arXiv version)
Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam, Gareth Speight. Warped products, solid hyperbolic fillings, and the identity D^(1,p)=N^(1,p)+R. Preprint. (2025) (link to arXiv version)

Accepted Publications

Josh Kline, Feng Li, Nageswari Shanmugalingam. Well-posedness of Dirichlet boundary value problems for reflected fractional p-Laplace-type inhomogeneous equations in compact doubling metric measure spaces. (To appear in) Calc. Var. Partial Differential Equations (2025) (link to arXiv version).
Sylvester Eriksson-Bique, Josh Kline. Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings. (To appear in) Indiana Univ. Math. J. (2025) (link to arXiv version).
Josh Kline, Pekka Koskela, Khanh Nguyen. Large-scale behaviour of Sobolev functions in Ahlfors regular metric measure spaces. J. Geom. Anal. 35 (2025) article no. 214 https://doi.org/10.1007/s12220-025-02052-x (link to arXiv version).
Josh Kline. Regularity of sets of finite fractional perimeter and nonlocal minimal surfaces in metric measure spaces. J. Geom. Anal. 35 (2025) article no. 182 https://doi.org/10.1007/s12220-025-02013-4 (link to arXiv version).
Luca Capogna, Josh Kline, Riikka Korte, Nageswari Shanmugalingam, Marie Snipes. Neumann problems for p-harmonic functions, and induced nonlocal operators on metric measure spaces. (To appear in) Amer. J. Math. (2025) (link to arXiv version)
Josh Kline, Antti Vähäkangas. Characterization of the upper Assouad codimension. J. Math. Soc. Japan 77, (2025) no. 4, pp. 1249-1267 (link to arXiv version).
Ivan Caamano, Josh Kline, Nageswari Shanmugalingam. Fine properties of metric space-valued functions of bounded variation in metric measure spaces. (To appear in) Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (2024) (link to arXiv version).
Josh Kline. Obstacle problems with double boundary condition for least gradient functions in metric measure spaces. Potential Anal. 62 (2024) no. 1, pp. 237-269 (link to arXiv version)
Ryan Gibara, Josh Kline. Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces. J. Funct. Anal. 285 (2023) Issue 10, 110126. (link to arXiv version).
Josh Kline. Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces. Rev. Mat. Iberoam. 39 (2023), no. 4, pp. 1567-1598 (link to arXiv version)
Josh Kline, Jeff Lindquist, Nageswari Shanmugalingam. Carathéodory-type extension theorem with respect to prime end boundaries. J. Geom. Anal. 31 (2021) pp. 4966–5009 (link to arXiv version)

Invited Talks

Self-improvement of fractional Hardy-inequalities in metric measure spaces via hyperbolic fillings. Quasiweekend III - Twenty Years On: Celebrating the Mathematics of Juha Heinonen, University of Helsinki, June 9, 2025.
Self-improvement of fractional Hardy inequalities in metric measure spaces. AMS Special Session - Nonsmooth Analysis and Geometry, AMS Fall Eastern Sectional Meeting, University of Albany, October 20, 2024.
On regularity of sets of finite fractional perimeter in metric measure spaces. AMS Special Session - Nonlocal Analysis and Geometric Measure Theory, AMS Fall Eastern Sectional Meeting, University of Albany, October 19, 2024.
Self-improvement of fractional Hardy inequalities in metric measure spaces. AMS-UMI Joint Meeting, Special Session - Nonlinear Problems with Nonstandard Growth Conditions and Analysis on Metric Spaces, Palermo University, July 2024.
On regularity of sets of finite fractional perimeter in metric measure spaces. AMS Special Session - Interactions between Analysis, Geometric Measure Theory, and Probability in Non-Smooth Spaces, AMS Spring Eastern Sectional Meeting, Howard University, April 6, 2024.
On regularity of sets of finite fractional perimeter in metric measure spaces. CMS Special Session - Harmonic Analysis and PDE, CMS Winter Meeting, Montreal, December 3, 2023.
Least gradient problems in metric measure spaces. Colloquium Series, Ball State University, November 16, 2023.
On regularity of sets of finite fractional perimeter in metric measure spaces. Analysis seminar, University of Tennessee, Knoxville, October 18, 2023.
On regularity of sets of finite fractional perimeter in metric measure spaces. Minisymposium - Interactions between analysis, optimization, and network science, SIAM Central States Section Annual Meeting, University of Nebraska, October 7, 2023.
On sets of finite fractional perimeter and the hyperbolic filling in metric measure spaces. NODE Seminar, Kansas State University, October 6, 2023.
On the nonlocal least gradient problem in metric measure spaces. OIST Workshop - Potential theory and random walks in metric spaces, Okinawa Institute of Science and Technology, June 2, 2023.
Obstacle problems with double boundary condition for least gradient functions in metric measure spaces. AMS Special Session - Interactions between Analysis, PDE, and Probability in Non-smooth Spaces, AMS Spring Central Sectional Meeting, University of Cincinnati, April 15, 2023.
Obstacle problems with double boundary condition for least gradient functions in metric measure spaces. Concentration Week on Analysis and Geometry of Nonsmooth Spaces, Texas A&M, August 2022.
Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions on metric measure spaces. Joint Mathematics Meeting (JMM), special session on “Analysis on Metric Spaces (a Mathematics Research Communities Session)” (Online) April 2022.

Other Talks

Trace and extension theorems for Besov functions in metric measure spaces. Ohio River Analysis Meeting, University of Cincinnati, March 30, 2025.
Self-improvement of fractional Hardy inequalities in metric measure spaces. Analysis Seminar, Kansas State University, October 4, 2024.
Self-improvement of fractional Hardy inequalities in metric measure spaces. Analysis Seminar, University of Cincinnati, September 30, 2024.
Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces. Ohio River Analysis Meeting, University of Kentucky, March 16, 2024.
On regularity of sets of finite fractional perimeter in metric measure spaces. Analysis Seminar, University of Cincinnati, February 29, 2024.
Least gradient problems in metric measure spaces. Analysis Seminar, University of Jyväskylä, Finland, May 10, 2023.
Obstacle problems with double boundary condition for least gradient functions in metric measure spaces. Ohio River Analysis Meeting, University of Cincinnati, March 2023.
Least gradient problems in metric measure spaces. UC Analysis Seminar, University of Cincinnati, October13, 2022.
Modulus in metric spaces. Analysis and Geometry of Random Spaces junior seminar, MSRI, Berkeley, CA, April 2022.
Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions on metric measure spaces. Ohio River Analysis Meeting, University of Kentucky, April 2022.

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