Nageswari Shanmugalingam

activity

20072026

most citedRegularity of sets with quasiminimal boundary surfaces in metric spaces

46 citations · 339 across the 63 of their papers we have counts for

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36 papers · 1 filter

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.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.MG2025

Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization

Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1

We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The go…

math.MG2024

On Carrasco Piaggio's theorem connecting combinatorial modulus and Ahlfors regular conformal dimension

Behnam Esmayli, Ryan Schardine, Nageswari Shanmugalingam

The goal of this paper is to provide an expository description of a result of Carrasco Piaggio connecting the Ahlfors regular conformal dimension of a compact uniformly perfect dou…

math.MG2024

On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry

Ryan Gibara, Ilmari Kangasniemi, Nageswari Shanmugalingam

We study the large-scale behavior of Newton-Sobolev functions on complete, connected, proper, separable metric measure spaces equipped with a Borel measure $μ$ with $μ (X) = \infty$ …

math.MG2023

Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry

Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1

We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equ…

math.MG2023

Construction of a Dirichlet form on metric measure spaces of controlled geometry

Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam

Given a compact doubling metric measure space $X$ that supports a $2$ -Poincaré inequality, we construct a Dirichlet form on $N^{1, 2} (X)$ that is comparable to the upper gradient en…

math.MG2023

Fine properties of metric space-valued mappings of bounded variation in metric measure spaces

Ivan Caamano, Josh Kline, Nageswari Shanmugalingam

Here we consider two notions of mappings of bounded variation (BV) from the metric measure space into the metric space; one based on relaxations of Newton-Sobolev functions, and th…

math.MG2023

Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a $p$ -Poincaré inequality

Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1

We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…

math.MG2022★ 3 cited

Potential theory and quasisymmetric maps between compact Ahlfors regular metric measure spaces via Besov functions: preliminary

Juha Lehrback, Nageswari Shanmugalingam

We study Besov capacities in a compact Ahlfors regular metric measure space by means of hyperbolic fillings of the space. This approach is applicable even if the space does not sup…

math.MG2022

On Carrasco Piaggio's theorem characterizing quasisymmetric maps from compact doubling spaces to Ahlfors regular spaces

Nageswari Shanmugalingam

In this note we deconstruct and explore the components of a theorem of Carrasco Piaggio, which relates Ahlfors regular conformal gauge of a compact doubling metric space to weights…

math.MG2022★ 1 cited

Conformal transformation of uniform domains under weights that depend on distance to the boundary

Ryan Gibara, Nageswari Shanmugalingam

The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected…

math.MG2021★ 6 cited

Classification of metric measure spaces and their ends using $p$ -harmonic functions

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$ -harmonic and $p$ -quasiharmonic functions, we classify proper metric spaces equipped…

math.MG2020★ 26 cited

Extension and trace results for doubling metric measure spaces and their hyperbolic fillings

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

In this paper we study connections between Besov spaces of functions on a compact metric space $Z$ , equipped with a doubling measure, and the Newton--Sobolev space of functions on…

math.MG2019★ 4 cited

Rough isometry between Gromov hyperbolic spaces and uniformization

Jeff Lindquist, Nageswari Shanmugalingam

In this note we show that given two complete geodesic Gromov hyperbolic spaces that are roughly isometric and $ε > 0$ , either the uniformization of both spaces with paramet…

math.MG2019★ 4 cited

BV functions and fractional Laplacians on Dirichlet spaces

Patricia Alonso Ruiz, Fabrice Baudoin, Li Chen +3

We study $L^{p}$ Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of he…

math.MG2019

Carathéodory-type extension theorem with respect to prime end boundaries

Joshua Kline, Jeff Lindquist, Nageswari Shanmugalingam

We prove a Carathéodory-type extension of BQS homeomorphisms between two domains in proper, locally path-connected metric spaces as homeomorphisms between their prime end closures.…

math.MG2019★ 6 cited

Bounded geometry and $p$ -harmonic functions under uniformization and hyperbolization

Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam

The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Astérisque {\bf 270} (2001), deal…

math.MG2019★ 1 cited

Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates

Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3

With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Di…

math.MG2018

Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3

We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a we…

math.MG2018★ 1 cited

Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces

Sylvester Eriksson-Bique, James T. Gill, Panu Lahti +1

In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a $1$ -Poincaré inequality. We show tha…

math.MG2018★ 10 cited

The Liouville theorem for $p$ -harmonic functions and quasiminimizers with finite energy

Anders Björn, Jana Björn, Nageswari Shanmugalingam

We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite $p$ th power energy in a (not necessarily complete) metric measure space equip…

math.MG2018★ 1 cited

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a $1$ -Poincaré inequality

Estibalitz Durand-Cartagena, Sylvester Eriksson-Bique, Riikka Korte +1

We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda~Jr. We show that these two notions coinc…

math.MG2018★ 1 cited

The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property

Tomasz Adamowicz, Nageswari Shanmugalingam

Prime end boundaries $\partial_{P} Ω$ of domains $Ω$ are studied in the setting of complete doubling metric measure spaces supporting a $p$ -Poincaré inequality. Notions of rectifiably…

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

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

Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization

On Carrasco Piaggio's theorem connecting combinatorial modulus and Ahlfors regular conformal dimension

On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry

Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry

Construction of a Dirichlet form on metric measure spaces of controlled geometry

Fine properties of metric space-valued mappings of bounded variation in metric measure spaces

Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a p-Poincaré inequality

Potential theory and quasisymmetric maps between compact Ahlfors regular metric measure spaces via Besov functions: preliminary

On Carrasco Piaggio's theorem characterizing quasisymmetric maps from compact doubling spaces to Ahlfors regular spaces

Conformal transformation of uniform domains under weights that depend on distance to the boundary

Classification of metric measure spaces and their ends using p-harmonic functions

Extension and trace results for doubling metric measure spaces and their hyperbolic fillings

Rough isometry between Gromov hyperbolic spaces and uniformization

BV functions and fractional Laplacians on Dirichlet spaces

Carathéodory-type extension theorem with respect to prime end boundaries

Bounded geometry and p-harmonic functions under uniformization and hyperbolization

Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates

Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces

The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality

The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property

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

Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a $p$ -Poincaré inequality

Classification of metric measure spaces and their ends using $p$ -harmonic functions

Bounded geometry and $p$ -harmonic functions under uniformization and hyperbolization

The Liouville theorem for $p$ -harmonic functions and quasiminimizers with finite energy

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a $1$ -Poincaré inequality