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

collaborators

70 papers

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.FA2026

On the equivalence of BV notions in metric measure spaces

Luigi Ambrosio, Enrico Pasqualetto, Nageswari Shanmugalingam

The aim of the paper is to compare in detail several notions of $B V$ space of functions of bounded variation in metric measure spaces $(X, d, m)$ . Informall…

math.AP2026

Approximation of harmonic functions on metric measure spaces of controlled geometry via discrete graphs

Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam

Given a complete doubling metric measure space $X$ that supports a $2$ -Poincaré inequality, we approximate harmonic functions on a bounded domain $Ω$ with a prescribed Newton-Sobol…

math.AP2026

Solving Dirichlet problem on unbounded uniform domains by using sphericalization techniques

Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1

Within the setting of metric spaces equipped with a doubling measure and supporting a $p$ -Poincaré inequality, establishing existence of solutions to Dirichlet problem in a bounded…

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.AP2025

Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

Luca Capogna, Ryan Gibara, Riikka Korte +1

We prove global Hölder regularity result for weak solutions $u \in N^{1, p} (Ω, μ)$ to a PDE of $p$ -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…

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.AP2024

Fractional $p$ -Laplacians via Neumann problems in unbounded metric measure spaces

Luca Capogna, Ryan Gibara, Riikka Korte +1

We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional $p$ -Laplace non-homogeneous equation $(- Δ_{p})^{s} u = f$ , with $0 < s < 1$ , $1 < p < \infty$ , for d…

math.FA2024★ 1 cited

Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces

Takashi Kumagai, Nageswari Shanmugalingam, Ryosuke Shimizu

In the context of a metric measure space $(X, d, μ)$ , we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of th…

math.AP2024

Well-posedness of Dirichlet boundary value problems for reflected fractional $p$ -Laplace-type inhomogeneous equations in compact doubling metric measure spaces

Josh Kline, Feng Li, Nageswari Shanmugalingam

In this paper we consider the setting of a locally compact, non-complete metric measure space $(Z, d, ν)$ equipped with a doubling measure $ν$ , under the condition that the boundary…

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.AP2024

On the Dirichlet-to-Neumann Map for the $p$ -Laplacian on a Metric Measure Space

Ryan Gibara, Nageswari Shanmugalingam

In this note, we construct a Dirichlet-to-Neumann map, from a Besov space of functions, to the dual of this class. The Besov spaces are of functions on the boundary of a bounded, l…

math.FA2023

Homogeneous Newton-Sobolev spaces in metric measure spaces and their Banach space properties

Nageswari Shanmugalingam

In this note we prove the Banach space properties of the homogeneous Newton-Sobolev spaces $H N^{1, p} (X)$ of functions on an unbounded metric measure space $X$ equipped with a doubl…

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.AP2023

Discontinuous eikonal equations in metric measure spaces

Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou

In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely $p$ -integrable in the domai…

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.FA2022★ 5 cited

Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces

Ryan Gibara, Nageswari Shanmugalingam

In this paper we fix $1 \leq p < \infty$ and consider $(\Om,d,μ)$ be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure $μ$ supporting a…

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.AP2022★ 5 cited

Solving a Dirichlet problem for unbounded domains via a conformal transformation

Ryan Gibara, Riikka Korte, Nageswari Shanmugalingam

In this paper, we solve the $p$ -Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure s…

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…

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

On the equivalence of BV notions in metric measure spaces

Approximation of harmonic functions on metric measure spaces of controlled geometry via discrete graphs

Solving Dirichlet problem on unbounded uniform domains by using sphericalization techniques

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

Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

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

Fractional p-Laplacians via Neumann problems in unbounded metric measure spaces

Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces

Well-posedness of Dirichlet boundary value problems for reflected fractional p-Laplace-type inhomogeneous equations in compact doubling metric measure spaces

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

On the Dirichlet-to-Neumann Map for the p-Laplacian on a Metric Measure Space

Homogeneous Newton-Sobolev spaces in metric measure spaces and their Banach space properties

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

Discontinuous eikonal equations 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

Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces

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

Solving a Dirichlet problem for unbounded domains via a conformal transformation

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

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

Fractional $p$ -Laplacians via Neumann problems in unbounded metric measure spaces

Well-posedness of Dirichlet boundary value problems for reflected fractional $p$ -Laplace-type inhomogeneous equations in compact doubling metric measure spaces

On the Dirichlet-to-Neumann Map for the $p$ -Laplacian on a Metric Measure Space

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