[shanmugal]

Full Professor, University of Cincinnati

**Email:** *shanmun AT uc.edu*

**Home-page:** https://homepages.uc.edu/~shanmun/

- A. Bjorn - J. Bjorn - N. Shanmugalingam (Submitted Paper)

Classification of metric measure spaces and their ends using $p$-harmonic functions (2021) - N. Shanmugalingam - Q. Liu - X. Zhou (Preprint)

Equivalence of solutions of eikonal equation in metric spaces (2020) - N. Shanmugalingam - J. Lindquist (Submitted Paper)

Traces and extensions of certain weighted Sobolev spaces on $\mathbb{R}^n$ and Besov functions on Ahlfors regular compact subsets of $\mathbb{R}^n$ (2020) - N. Shanmugalingam - J. Bjorn - A. Bjorn (Submitted Paper)

Extension and trace results for doubling metric measure spaces and their hyperbolic fillings (2020) - S. Eriksson-Bique - G. Giovannardi - R. Korte - N. Shanmugalingam - G. Speight (Preprint)

Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry (2020) - N. Shanmugalingam (Proceedings)

$p$-hyperbolicity of ends and families of paths in metric spaces (2019) - E. Durand-Cartagena - S. Eriksson-Bique - R. Korte - N. Shanmugalingam (Accepted Paper:
*Advances in Calculus of Variations*)

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a $1$-Poincaré inequality (2019) - P. Lahti - R. Jones - N. Shanmugalingam (Accepted Paper:
*Indiana University Math. J.*)

Modulus of families of sets of finite perimeter and quasiconformal maps between metric spaces of globally $Q$-bounded geometry (2019) - L. Malý - N. Shanmugalingam (
*J. Diff. Eq.*)

Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity (2018) - P. Lahti - N. Shanmugalingam (
*J. Funct. Anal.*)

Trace theorems for functions of bounded variation in metric spaces (2018) - N. Shanmugalingam - P. Lahti - L. Malý - G. Speight (Accepted Paper:
*Journal of Geometric Analysis*)

Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient (2018) - E. Durand-Cartagena - J. Á. Jaramillo - N. Shanmugalingam (Accepted Paper:
*Mathematische Annalen*)

Existence and uniqueness of $\infty$-harmonic functions under assumption of $\infty$-Poincaré inequality (2018) - S. Eriksson-Bique - J. Gill - P. Lahti - N. Shanmugalingam (Preprint)

Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces (2018) - R. Korte - P. Lahti - X. Li - N. Shanmugalingam (Accepted Paper:
*Revista Mat. Iberoamericana*)

Notions of Dirichlet problem for functions of least gradient in metric measure spaces (2017) - N. Marola - M. Miranda Jr - N. Shanmugalingam (Online First Paper:
*Potential Analysis*)

Characterizations of sets of finite perimeter using heat kernels in metric spaces (2016) - L. Malý - N. Shanmugalingam - M. Snipes (Accepted: 2016:
*Annali SNS.*)

Trace and extension theorems for functions of bounded variation (2016) - E. Durand-Cartagena - J. Á. Jaramillo - N. Shanmugalingam (
*Pub. Mat.*)

Geometric characterizations of $p$-Poincaré inequalities (2016) - H. Aikawa - A. Bjorn - J. Bjorn - N. Shanmugalingam (
*Advances in Calc. Var.*)

DICHOTOMY OF GLOBAL CAPACITY DENSITY IN METRIC MEASURE SPACES (2016) - J. Kinnunen - R. Korte - N. Marola - N. Shanmugalingam (To appear:
*Collect. Math.*)

A characterization of BMO self-maps of a metric measure space (2015) - N. Shanmugalingam - P. Lahti - R. Korte - H. Hakkarainen (Published:
*Analysis and Geometry in Metric Spaces*)

Stability and continuity of functions of least gradient (2015) - R. Korte - P. Lahti - N. Shanmugalingam (Accepted Paper:
*Calc. Var. PDE*)

Semmes family of curves and a characterization of functions of bounded variation in terms of curves (2015) - N. Marola - M. Miranda Jr - N. Shanmugalingam (Accepted:
*Revista Mathematica Iberoamericana*)

Boundary measures, generalized Gauss-Green formulas and the mean value property in metric measure spaces (2014) - E. Durand-Cartagena - J. Á. Jaramillo - N. Shanmugalingam (
*Ann. Ac. Sci. Fen. Math.*)

First order Poincaré inequalities in metric measure spaces (2013) - J. Kinnunen - R. Korte - A. Lorent - N. Shanmugalingam (
*J. Geom. Anal.*)

Regularity of sets with quasiminimal boundary surfaces in metric spaces (2013) - R. Korte - N. Marola - N. Shanmugalingam (
*Ark. Mat.*)

Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property (2012) - E. Durand-Cartagena - N. Shanmugalingam - A. Williams (
*Math. Z.*)

$p$-Poincaré inequality vs. infinity-Poincaré inequality; some counter-examples (2012) - P. Koskela - M. Miranda Jr - N. Shanmugalingam (
*International Mathematical Series (N.Y.)*)

Geometric properties of planar BV-extension domains (2010)

*10 oct 2011 - 14 oct 2011:*ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

*1 sep 2019 - 30 nov 2019:*Simons Semester in Geometry and Analysis