Panu Lahti's research page

Contact information

Email: panulahti@amss.ac.cn

Affiliation

    I am an associate professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences. I did my doctoral studies at Aalto University.

Research interests

• Analysis on metric measure spaces

• Functions of bounded variation (BV functions)

• Fine potential theory for p=1

• Maximal functions

• Nonlocal functionals

  I am interested in characterization and approximation results for functions of bounded variation (BV functions) and in fine potential theory in the case p=1. Many of these results seem to be new even in Euclidean spaces, but it is natural to study them in the more general setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality. Recently I have worked especially on characterizations of BV functions by means of nonlocal functionals. I am also interested in quasiconformal mappings in metric spaces, as well as the so-called W1,1-problem for the (non-centered) maximal function.

Publications

2023

• 40. A Bjorn, J. Bjorn, and P. Lahti, Removable sets for Newtonian Sobolev spaces and a characterization of p-path almost open sets, Rev. Mat. Iberoam. 39 (2023), no. 3, 1143–1180.

• 39. P. Lahti, A note on indecomposable sets of finite perimeter, Adv. Calc. Var. 16 (2023), no. 3, 559–570.

• 38. P. Lahti, Capacitary density and removable sets for Newton-Sobolev functions in metric spaces, Calc. Var. Partial Differential Equations 62 (2023), no.5, Paper No. 155, 20 pp.

• 37. P. Lahti, On rough traces of BV functions, J. Math. Pures Appl. (9) 170 (2023), 33–56.

• 36. P. Lahti and X. Zhou, Absolutely continuous mappings on doubling metric measure spaces, to appear in Manuscripta mathematica.

2022

• 35. L. Beck and P. Lahti, A note on the weak* and pointwise convergence of BV functions, Nonlinear Anal. 225 (2022), Paper No. 113028, 20 pp.

2021

• 34. S. Eriksson-Bique, J. T. Gill, P. Lahti, and N. Shanmugalingam, Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces. Trans. Amer. Math. Soc. 374 (2021), no. 11, 8201–8247.

• 33. P. Lahti, On the regularity of the maximal function of a BV function, J. Differential Equations 300 (2021), 53–79. 

• 32. P. Lahti, The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces,  Adv. Calc. Var. 14 (2021), no. 2, 171–192.

• 31. P. Lahti, X. Li, and Z. Wang, Traces of Newton-Sobolev, Hajlasz-Sobolev, and BV functions on metric spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 3, 1353–1383.

• 30. P. Lahti and X. Zhou, Functions of bounded variation on complete and connected one-dimensional metric spaces.Int. Math. Res. Not. IMRN 2021, no. 20, 15412–15443.

2020

• 29. R. Jones and P. Lahti, Duality of moduli and quasiconformal mappings in metric spaces, Anal. Geom. Metr. Spaces 8 (2020), no. 1, 166–181.

• 28. R. Jones, P. Lahti, and N. Shanmugalingam, Modulus of families of sets of finite perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry, Indiana Univ. Math. J. 69 (2020), no. 1, 265–294.

• 27. P. Lahti, A new Federer-type characterization of sets of finite perimeter in metric spaces, Arch. Ration. Mech. Anal. 236 (2020), no. 2, 801–838.

• 26. P. Lahti, A sharp Leibniz rule for BV functions in metric spaces, Rev. Mat. Complut. 33 (2020), no. 3, 797–816.

• 25. P. Lahti, Approximation of BV by SBV functions in metric spaces, J. Funct. Anal. 279 (2020), no. 11, 108763, 33 pp.

• 24. P. Lahti, Capacities and 1-strict subsets in metric spaces, Nonlinear Analysis, Volume 192, March 2020.

• 23. P. Lahti, Discrete convolutions of BV functions in quasiopen sets in metric spaces, Calc. Var. Partial Differential Equations 59 (2020), no. 1, Paper No. 27, 23 pp.

• 22. P. Lahti, Federer's characterization of sets of finite perimeter in metric spaces, Analysis & PDE, Vol. 13 (2020), No. 5, 1501–1519.

• 21. P. Lahti, Quasiopen sets, bounded variation and lower semicontinuity in metric spaces, Potential Anal. 52 (2020), no. 2, 321–337.

• 20. P. Lahti, Superminimizers and a weak Cartan property for p=1 in metric spaces, J. Anal. Math. 140 (2020), no. 1, 55–87.

2019

• 19. R. Korte, P. Lahti, X. Li, and N. Shanmugalingam, Notions of Dirichlet problem for functions of least gradient in metric measure spaces, Rev. Mat. Iberoam. 35 (2019), no. 6, 1603–1648.

• 18. P. Lahti, The Choquet and Kellogg properties for the fine topology when p=1 in metric spaces, Journal de Mathématiques Pures et Appliquées, Volume 126, June 2019, Pages 195-213.

• 17. P. Lahti, L. Maly, N. Shanmugalingam, and G. Speight, Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient, The Journal of Geometric Analysis, December 2019, Volume 29, Issue 4, pp 3176–3220.

2018

• 16. P. Lahti, A new Cartan-type property and strict quasicoverings when p=1 in metric spaces, Ann. Acad. Sci. Fenn. Math. 43 (2018), pp. 1027–1043.

• 15. P. Lahti, Strong approximation of sets of finite perimeter in metric spaces, Manuscripta Math. 155 (2018), no. 3-4, 503–522.

• 14. P. Lahti, L. Maly, and N. Shanmugalingam, An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability, Anal. Geom. Metr. Spaces 6 (2018), 1–31.

• 13. P. Lahti and N. Shanmugalingam, Trace theorems for functions of bounded variation in metric spaces, J. Funct. Anal. 274 (2018), no. 10, 2754–2791.

2017

• 12. P. Lahti, A Federer-style characterization of sets of finite perimeter on metric spaces, Calc. Var. Partial Differential Equations, October 2017, 56:150.

• 11. P. Lahti, A notion of fine continuity for BV functions on metric spaces, Potential Analysis, February 2017, Volume 46, Issue 2, pp 279–294.

• 10. P. Lahti, Strict and pointwise convergence of BV functions in metric spaces, Journal of Mathematical Analysis and Applications, Volume 455, Issue 2, 15 November 2017, Pages 1005–1021.

• 9. P. Lahti and N. Shanmugalingam, Fine properties and a notion of quasicontinuity for BV functions on metric spaces, Journal de Mathématiques Pures et Appliquées, Volume 107, Issue 2, February 2017, Pages 150–182.

2016

• 8. H. Hakkarainen, J. Kinnunen, P. Lahti, and P. Lehtela, Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces, Anal. Geom. Metr. Spaces 4 (2016), Art. 13.

• 7. J. Kristensen and P. Lahti, Lower semicontinuity for an integral functional in BV, Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 70, 23 pp.

2015

• 6. H. Hakkarainen, J. Kinnunen and P. Lahti, Regularity of minimizers of the area functional in metric spaces, Adv. Calc. Var. 8 (2015), no. 1, 55-68.

• 5. H. Hakkarainen, R. Korte, P. Lahti, and N. Shanmugalingam, Stability and continuity of functions of least gradient, Anal. Geom. Metr. Spaces 3 (2015), 123-139.

• 4. R. Korte, P. Lahti, and N. Shanmugalingam, Semmes family of curves and a characterization of functions of bounded variation in terms of curves, Calc. Var. Partial Differential Equations 54 (2015), no. 2, 1393–1424.

• 3. P. Lahti, Extensions and traces of functions of bounded variation on metric spaces, Journal of Mathematical Analysis and Applications, Volume 423, Issue 1, 1 March 2015, Pages 521–537.

2014

• 2. R. Korte and P. Lahti, Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces, Annales de l'Institut Henri Poincaré Non Linear Analysis, Volume 31, Issue 1, January-February 2014, Pages 129–154.

• 1. P. Lahti and H. Tuominen, A pointwise characterization of functions of bounded variation on metric spaces, Ric. Mat. 63 (2014), no. 1, 47–57.

Theses

• Doctoral Thesis (2014)

• Master's Thesis (2011)