Panu Lahti

activity

20132026

most citedNotions of Dirichlet problem for functions of least gradient in metric measure spaces

15 citations · 54 across the 42 of their papers we have counts for

collaborators

52 papers

math.CA2026

Functions of bounded variation are not dense in the Strong BD Norm

Panu Lahti, Quoc-Hung Nguyen

We prove that functions of bounded variation are not dense in the space of functions of bounded deformation with respect to the strong BD norm. Using alternating Riesz products and…

math.FA2026

Decomposition of functions of bounded variation in Ahlfors-regular PI spaces

Paolo Bonicatto, Panu Lahti, Enrico Pasqualetto

We prove that, on a non-compact Ahlfors-regular PI space, every function of bounded variation $f$ can be decomposed as a countable sum $\sum_{n = 1}^{\infty} f_{n}$ of monotone functions…

math.FA2026

Boxing inequalities for relative fractional perimeter and fractional Poincaré-type inequalities on John domains with the BBM factor

Manzi Huang, Panu Lahti, Jiang Li +1

For $0 < δ, τ < 1$ and $1 \leq s \leq \frac{n}{n - δ}$ , we prove that for a given $s$ -John domain $Ω \subset R^{n}$ , the following Boxing inequality holds for every Lebesgue measurable…

math.MG2025

A topological characterization of indecomposable sets of finite perimeter

Paolo Bonicatto, Panu Lahti, Enrico Pasqualetto

We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topologica…

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.CA2025

The centered maximal operator removes the non-concave Cantor part from the gradient

Panu Lahti, Julian Weigt

We study regularity of the centered Hardy--Littlewood maximal function $M f$ of a function $f$ of bounded variation in $R^{d}$ , $d \in N$ . In particular, we show that…

math.CA2024

Quasiconformal mappings and the rank of $\frac{d D f}{d ∣ D f ∣}$ for $f \in B V (R^{n}; R^{n})$

Panu Lahti

We define a relaxed version $H_{f}^{fine}$ of the distortion number $H_{f}$ that is used to define quasiconformal mappings. Then we show that for a BV function $f\in BV(\mathb…

math.FA2023

BV functions and nonlocal functionals in metric measure spaces

Panu Lahti, Andrea Pinamonti, Xiaodan Zhou

We study the asymptotic behavior of three classes of nonlocal functionals in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. We show t…

math.AP2023

BMO-type functionals, total variation, and $Γ$ -convergence

Panu Lahti, Quoc-Hung Nguyen

We study the BMO-type functional $κ_{ε} (f, R^{n})$ , which can be used to characterize BV functions $f \in B V (R^{n})$ . The $Γ$ -limit of this functional, taken wi…

math.MG2023

Alberti's rank one theorem and quasiconformal mappings in metric measure spaces

Panu Lahti

We investigate a version of Alberti's rank one theorem in Ahlfors regular metric spaces, as well as a connection with quasiconformal mappings. More precisely, we give a proof of th…

math.MG2022★ 1 cited

Capacitary density and removable sets for Newton-Sobolev functions in metric spaces

Panu Lahti

In a complete metric space equipped with a doubling measure and supporting a $(1, 1)$ -Poincaré inequality, we show that every set satisfying a suitable capacitary density condition…

math.MG2022★ 1 cited

Finely quasiconformal mappings

Panu Lahti

We introduce a relaxed version of the metric definition of quasiconformality that is natural also for mappings of low regularity, including $W_{\mathrm{loc}}^{1,1}(\mathbb{R}^n;\ma…

math.FA2022

A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces

Panu Lahti, Andrea Pinamonti, Xiaodan Zhou

We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Compared wi…

math.MG2022

Quasiconformal, Lipschitz, and BV mappings in metric spaces

Panu Lahti

Consider a mapping $f : X \to Y$ between two metric measure spaces. We study generalized versions of the local Lipschitz number $Lip f$ , as well as of the distortion nu…

math.MG2022

Generalized Lipschitz numbers, fine differentiability, and quasiconformal mappings

Panu Lahti

We introduce a generalized version of the local Lipschitz number $lip u$ , and show that it can be used to characterize Sobolev functions $u\in W_{\textrm{loc}}^{1,p}(\mat…

math.FA2021

Absolutely continuous mappings on doubling metric measure spaces

Panu Lahti, Xiaodan Zhou

Following Malý's definition of absolutely continuous functions of several variables, we consider $Q$ -absolutely continuous mappings $f : X \to V$ between a doubling metric measu…

math.MG2021

Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces

Panu Lahti, Xiaodan Zhou

Given a homeomorphism $f : X \to Y$ between $Q$ -dimensional spaces $X, Y$ , we show that $f$ satisfying the metric definition of quasiconformality outside suitable exceptional set…

math.FA2021

On rough traces of BV functions

Panu Lahti

In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincaré inequality, but possibly having a very larg…

math.MG2021

Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces

Panu Lahti, Xiaodan Zhou

We show that a mapping $f : X \to Y$ satisfying the metric condition of quasiconformality outside suitable exceptional sets is in the Newton-Sobolev class $N_{\textrm{loc}}^{1,1…

math.AP2021★ 7 cited

Removable sets for Newtonian Sobolev spaces and a characterization of $p$ -path almost open sets

Anders Björn, Jana Björn, Panu Lahti

We study removable sets for Newtonian Sobolev functions in metric measure spaces satisfying the usual (local) assumptions of a doubling measure and a Poincaré inequality. In partic…

math.MG2021

A note on indecomposable sets of finite perimeter

Panu Lahti

Bonicatto--Pasqualetto--Rajala (2020) proved that a decomposition theorem for sets of finite perimeter into indecomposable sets, known to hold in Euclidean spaces, holds also in co…

math.FA2020

A note on the weak* and pointwise convergence of BV functions

Lisa Beck, Panu Lahti

We study pointwise convergence properties of weakly* converging sequences ${u_{i}}_{i \in N}$ in $BV (R^{n})$ . We show that, after passage to a suitable s…

math.CA2020

On the regularity of the maximal function of a BV function

Panu Lahti

We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{if} the non-centered maximal functions of an SBV function is a BV functi…

math.MG2019★ 7 cited

Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces

Panu Lahti, Xining Li, Zhuang Wang

We study the boundary traces of Newton-Sobolev, Hajlasz-Sobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature…

Functions of bounded variation are not dense in the Strong BD Norm

Decomposition of functions of bounded variation in Ahlfors-regular PI spaces

Boxing inequalities for relative fractional perimeter and fractional Poincaré-type inequalities on John domains with the BBM factor

A topological characterization of indecomposable sets of finite perimeter

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

The centered maximal operator removes the non-concave Cantor part from the gradient

Quasiconformal mappings and the rank of d∣Df∣dDf​ for f∈BV(Rn;Rn)

BV functions and nonlocal functionals in metric measure spaces

BMO-type functionals, total variation, and Γ-convergence

Alberti's rank one theorem and quasiconformal mappings in metric measure spaces

Capacitary density and removable sets for Newton-Sobolev functions in metric spaces

Finely quasiconformal mappings

A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces

Quasiconformal, Lipschitz, and BV mappings in metric spaces

Generalized Lipschitz numbers, fine differentiability, and quasiconformal mappings

Absolutely continuous mappings on doubling metric measure spaces

Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces

On rough traces of BV functions

Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces

Removable sets for Newtonian Sobolev spaces and a characterization of p-path almost open sets

A note on indecomposable sets of finite perimeter

A note on the weak* and pointwise convergence of BV functions

On the regularity of the maximal function of a BV function

Traces of Newton-Sobolev, Hajlasz-Sobolev and BV functions on metric spaces

Quasiconformal mappings and the rank of $\frac{d D f}{d ∣ D f ∣}$ for $f \in B V (R^{n}; R^{n})$

BMO-type functionals, total variation, and $Γ$ -convergence

Removable sets for Newtonian Sobolev spaces and a characterization of $p$ -path almost open sets