List of papers of Nages Shanmugalingam

My research area is geometric function theory. I am interested in the connection between inequalities in analysis and their geometric implications, and also in quasiconformal maps and the geometric properties of metric measure spaces conserved by them. Currently I am also involved in the studying interactions between geometry and the BV theory in metric spaces, and the utility of sets of finite perimeter in the study of Sobolev spaces.

My thesis, 1999, at the University of Michigan.

List of papers:

Newton-Sobolev spaces for metric measure spaces:

1. Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
appeared in Rev. Mat. Iberoamericana, 16 (2000) 243--279.

2. Removable sets for the Poincare inequality on metric spaces
(with Pekka Koskela and Heli Tuominen)
appeared in Indiana Univ. Math. J., 49 (2000) 333--352.

3. Modulus and continuous capacity
(with Sari kallunki)
appeared in Ann. Acad. Sci. Fenn. Math., 26 (2001) 455--464.

4. Sobolev classes of Banach space-valued functions and quasiconformal mappings
(with Juha Heinonen, Pekka Koskela, and Jeremy Tyson)
appeared in J. Anal. Math., 85 (2001) 87--139.

5. Measurability of equivalence classes and $MEC_p$-property in metric spaces
(with Esa Järvenpää, Maarit Järvenpää, Kevin Rogovin, and Sari Rogovin.)
appeared in Rev. Mat. Iberoamericana, 23 no. 3 (2007) 811--830.

6. Sobolev extensions of Hölder continuous and characteristic functions on metric spaces
(with Anders Björn and Jana Björn)
appeared in Canadian Journal of Mathematics, 59 (No. 6) (2007), 1135--1153.

7. Poincare inequalities, uniform domains, and extension properties for Newton-Sobolev spaces in metric spaces
(with Jana Björn)
appeared in J. Math. Anal. Appl., 332, No. 1 (2007) 190--208.

8. Quasicontinuity of Newton--Sobolev functions and density of Lipschitz functions in metric measure spaces
(with Anders Björn and Jana Björn)
appeared in Houston J. Math., 34 No. 4 (2008) 1197--1211.

9. Lebesgue points and capacities via boxing inequalities in metric spaces
(with Juha Kinnunen, Riikka Korte, and Heli Tuominen)
appeared in Indiana Univ. Math. J., 57 no. 1 (2008) 401-430.

10. Interpolation properties of Besov spaces defined on metric spaces
(with Pekka Koskela and Amiran Gogatishvili)
Math. Nachr., to appear.

11. Geometric properties of planar BV extension domains
(with Pekka Koskela and Michele Miranda)
to appear, Function Spaces; Topics Around the Research of Prof. Maz'ya I,
International Mathematical Series (Springer collection).

12. The DeGiorgi measure and an obstacle problem related to minimal surfaces in metric spaces,
(with Juha Kinnunen, Riikka Korte, and Heli Tuominen)
, to appear in J. Math. Pures Appl.

$p$-harmonic functions in metric measure spaces:

1. Harmonic functions on metric spaces
appeared in Illinois J. Math., 45 no. 3 (2001) 1021--1050.

2. Regularity of quasi-minimizers on metric spaces
(with Juha Kinnunen)
appeared in Manuscripta Math., 105 (2001) 401--423.

3. Fat sets and pointwise boundary estimates for $p$-harmonic functions in metric spaces
(with Jana Björn and Paul MacManus)
appeared in J. Anal. Math., 85 (2001) 339--369.

4. The Dirichlet problem for $p$-harmonic functions on metric measure spaces
(with Anders Björn and Jana Björn)
appeared in J. Reine Angew. Math. (Crelle) 556 (2003) 173--203.

5. Some convergence results for $p$-harmonic functions on metric measure spaces
appeared in the Proceedings of the London Math. Soc. 87 (2003) 226--246.

6. The Perron method for $p$-harmonic functions in metric spaces
(with Anders Björn and Jana Björn)
appeared in J. Differential Equations 195 (2003) 398--429.

7. A problem of Baernstein on the equality of the $p$-harmonic measure of a set and its closure
(with Anders Björn and Jana Björn)
appeared in Proc. Amer. Math. Soc. 134 (2006) 509-519.

8. Hölder estimates of $p$-harmonic extension operators
(PDF file) (with Hiroaki Aikawa)
appeared in J. Differential Equations 220 (2006) No. 1, 18--45.

9. Polar sets on metric spaces
(with Juha Kinnunen)
appeared in Transactions Amer. Math. Soc. 358 (2006) 11--37.

10. Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces (pdf file)
(with Petri Juutinen)
appeared in Math. Nachr. 279 (2006) 1083--1098.

11. Maximal regularity via reverse Holder inequalities for elliptic systems of $n$-Laplace type involving measures, (with Xiao Zhong and Tero Kilpeläinen)
appeared in Ark. Mat. 46 (No. 1) (2008) 77--93.

12. Equivalence and self-improvement of $p$-fatness and Hardy's inequality, and association with uniform perfectness
(with Riikka Korte)
Math. Z. , to appear.

Conformal Martin boundary:

1. Singular functions on metric measure spaces
(with Ilkka Holopainen)
appeared in Collect. Math., 53 (2002) 313--332.

2. On the conformal Martin boundary of domains in metric spaces
(with Ilkka Holopainen and Jeremy Tyson)
appeared in Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday Report. Univ. Jyväskylä 83 (2001) 147--168.

3. Singular behavior of conformal Martin kernels, and non-tangential limits of conformal mappings
appeared in Ann. Acad. Sci. Fenn. Math. 29 (2004) 195--210.

4. Carleson type estimates for $p$-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces.
(with Hiroaki Aikawa)
appeared in Michigan Math. J. 53 (2005) 165--188.

5. Boundary Harnack principle for $p$-harmonic functions in smooth Euclidean domains
(with Hiroaki Aikawa, Tero Kilpeläinen, and Xiao Zhong),
appeared in Potential Analysis 26 No.3 (2007) 281--301.

6. Uniformity from Gromov hyperbolicity
(with David Herron and Xiangdong Xie),
to appear in Illinois J. Math..

Dirichlet forms on metric measure spaces:

1. Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
(with Pekka Koskela and Kai Rajala)
appeared in J. Funct. Anal. 202 (2003) 147--173.

2. Dirichlet forms, Poincare inequalities, and the Sobolev spaces of Korevaar-Schoen
(with Pekka Koskela and Jeremy Tyson)
appeared in Potential Analysis. 21 No.3 (2004) 241--262.

3. A universality property of Sobolev spaces in metric measure spaces
appeared in the Springer collection Sobolev Spaces in Mathematics I, II, III (2009)
of the International Mathematical Series.

Last updated 28 September 2009.
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