Panu Lahti's research page

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Affiliation

I am about to start as assistant professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences. I did my doctoral studies at Aalto University and I collaborate mainly with members of the Nonlinear PDE Research Group.

Research interests

  • Analysis on metric measure spaces
  • Functions of bounded variation (BV functions)
  • Fine potential theory for p=1
  • Quasiconformal mappings

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. I am also interested in quasiconformal mappings, in particular in connection with sets of finite perimeter.

Publications

Preprints

  1. 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, preprint 2018.
  2. P. Lahti, On the regularity of the maximal function of a BV function, preprint 2020.

2020

  1. R. Jones and P. Lahti, Duality of moduli and quasiconformal mappings in metric spaces, to appear in Analysis and Geometry in Metric Spaces.
  2. P. Lahti, Approximation of BV by SBV functions in metric spaces, to appear in Journal of Functional Analysis.
  3. 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.
  4. P. Lahti, Capacities and 1-strict subsets in metric spaces, Nonlinear Analysis, Volume 192, March 2020.
  5. 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.
  6. P. Lahti, Quasiopen sets, bounded variation and lower semicontinuity in metric spaces, Potential Anal. 52 (2020), no. 2, 321–337.
  7. P. Lahti, Superminimizers and a weak Cartan property for p=1 in metric spaces, J. Anal. Math. 140 (2020), no. 1, 55–87.
  8. P. Lahti, X. Li, and Z. Wang, Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces, to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
  9. P. Lahti and X. Zhou, Functions of bounded variation on complete and connected one-dimensional metric spaces, to appear in International Mathematics Research Notices.

2019

  1. 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, to appear in Indiana University Mathematics Journal.
  2. 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.
  3. P. Lahti, A sharp Leibniz rule for BV functions in metric spaces, to appear in Revista Matemática Complutense.
  4. P. Lahti, Federer's characterization of sets of finite perimeter in metric spaces, to appear in Analysis & PDE.
  5. 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.
  6. P. Lahti, L. Malý, 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

  1. 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.
  2. P. Lahti, Strong approximation of sets of finite perimeter in metric spaces, Manuscripta Math. 155 (2018), no. 3-4, 503–522.
  3. P. Lahti, The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces, Advances in Calculus of Variations.
  4. P. Lahti, L. Malý, 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.
  5. 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

  1. P. Lahti, A Federer-style characterization of sets of finite perimeter on metric spaces, Calc. Var. Partial Differential Equations, October 2017, 56:150.
  2. P. Lahti, A notion of fine continuity for BV functions on metric spaces, Potential Analysis, February 2017, Volume 46, Issue 2, pp 279–294.
  3. 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.
  4. 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

  1. H. Hakkarainen, J. Kinnunen, P. Lahti, and P. Lehtelä, Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces, Anal. Geom. Metr. Spaces 4 (2016), Art. 13.
  2. 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

  1. 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.
  2. 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.
  3. 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.
  4. 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

  1. 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.
  2. 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