Full Professor, University of Cincinnati

Email: shanmun AT uc.edu

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

Available papers (27):

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• 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)

Seminars:

• 14 may 2018: Geometric and analytic aspects of $\infty$-Poincar\'e inequalities

Speaker:

• 16 jun 2025 - 18 jun 2025: Three days in Sub-Riemannian geometry
• 1 jun 2025 - 7 jun 2025: Spring School on Analysis 2025: Function Spaces and Applications XIII
• 21 may 2024 - 24 may 2024: Workshop: Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension
• 10 oct 2011 - 14 oct 2011: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Organizer:

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