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Nageswari Shanmugalingam
Associate Professor
814 Old Chemistry Building
513-556-4062
shanmun@uc.edu
http://math.uc.edu/~nages
Professional Summary
I received my Bachelors degree from the University of Rochester in 1994 and my doctoral degree from the University of Michigan in 1999, under the supervision of Professor Juha Heinonen.
Education
Ph.D, University of Michigan at Ann Arbor, 1999.
Research Interests
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. Just as a geometer cannot distinguish between the flat torus and a torus with non-zero curvature without the aid of a metric on the torus, neither can a metric space analyst distinguish different geometries on the same metric measure space without corresponding differential operators. Such different operators can be constructed for certain metric measure spaces; this is a result due to Cheeger. I am also interested in studying the different geometries on a metric measure space given by different Cheeger differential structures.
Research Support
Taft Research Seminar fund, Funded 08-2005 to 05-2006.
NSF grant , (DMS–0355027 ); 98481. Funded 08-2004 to 08-2008.
NSF grant , (DMS–0100132/0243355 ); 65061. Funded 08-2001 to 08-2004.
European Union CMU grant, University of Jyv¨askyl¨a. Funded 01-2001 to 05-2001.
Post-doctoral visiting fellowship, Mittag-Leffler Institute. Funded 09-1999 to 12-1999.
Wilson Scholarship , University of Rochester. Funded 01-1993 to 05-1994.
Peer Reviewed Publications
Bjorn, Jana (2007). Poincare inequalities, uniform domains, and extension properties for Newton-Sobolev spaces in metric spaces. J. Math. Anal. Appl., 332, 190–208.
Aikawa, Hiroaki, Kilpel¨ainen, Tero, & Zhong, Xiao (2007). Boundary Harnack principle for p-harmonic functions in smooth Euclidean domains. Potential Analysis, 26, 281–301.
Kinnunen, Juha (2006). Polar sets on metric spaces. Transactions Amer. Math. Soc., 358, 11–37.
Aikawa, Hiroaki (2006). H¨older estimates of p-harmonic extension operators. J. Differential Equations, 220, 18–45.
Bjorn, Anders, & Bjorn, Jana (2006). A problem of Baernstein on the equality of the p-harmonic measure of a set and its closure. Proc. Amer. Math. Soc., 134, 509–519.
Juutinen, Petri (2006). Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces. Math. Nachr., 279, 1083–1098.
Aikawa, Hiroaki (2005). Carleson type estimates for p-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces. Michigan Math. J., 53, 165–188.
Koskela, Pekka, & Tyson, Jeremy (2004). Dirichlet forms, Poincar inequalities and the Sobolev spaces of Korevaar-Schoen. Potential Analysis, 21, 241–262.
(2004). Singular behavior of conformal Martin kernels, and non-tangential limits of conformal mappings. Ann. Acad. Sci. Fenn. Math., 29, 195–210.
(2003). Some convergence results for p-harmonic functions on metric measure spaces. Proc. London Math. Soc., 87, 226-246.
Bjorn, Anders, & Bjorn, Jana (2003). The Dirichlet problem for p-harmonic functions on metric measure spaces. J. Reine Angew. Math.(Crelle), 556, 173-203.
Koskela, Pekka, & Rajala, Kai (2003). Lipschitz continuity of Cheeger harmonic functions in metric measure spaces. J. Funct. Anal., 202, 147-173.
Bjorn, Anders, & Bjorn, Jana (2003). The Perron method for p-harmonic functions in metric spaces. J. Differential Equations, 195, 398–429.
(2003). RNC Workshop: Potential theory in metric spaces. Report of Univ. Jyv¨askyl¨a Dept. Math. Stat., 92, 243–248.
Holopainen, Ilkka (2002). Singular functions on metric measure spaces. Collect. Math., 53, 313–332.
(2001). Harmonic functions on metric spaces. Illinois J. Math., 45, 1021–1050.
Kallunki, Sari (2001). Modulus and continuous capacity. Ann. Acad. Sci. Fenn. Math., 26, 455–464.
Kinnunen, Juha (2001). Regularity of quasiminimizers on metric spaces. Manuscripta Mathematica, 105, 401-423.
Heinonen, Juha, Koskela, Pekka, & Tyson, Jeremy (2001). Sobolev classes of Banach space-valued functions and quasiconformal mappings. J. Analyse Math., 85, 87-139.
Bjorn, Jana, & MacManus, Paul (2001). Fat sets and point-wise boundary estimates for p-harmonic functions in metric spaces. J. Analyse Math., 85, 339–369.
Holopainen, Ilkka, & Tyson, Jeremy (2001). On the conformal Martin boundary of domains in metric spaces. Papers on Analysis, Report Univ. Jyv¨askyl¨a, 83, 147–168.
(2000). Newtonian Spaces: An extension of Sobolev spaces to metric measure spaces. Revista Matematica Iberoamericana, 16, 243–279.
Koskela, Pekka, & Tuominen, Heli (2000). Removable sets for the Poincar´e inequality on metric spaces. Indiana University Mathematics Journal, 49, 333–352.
Invited Presentations
(06-2007). Mini-course on BV functions in metric spaces. Helsinki University of Technology
(05-2007). Boxing inequalities and characterizing 1-hyperbolicity. International Conference on Harmonic Analysis, Pescara, Italy.
(05-2007). Analysis seminar. University of Pisa, Pisa, Italy.
(04-2007). Analysis seminar. University of Jyv¨askyl¨a, Finland.
(11-2006). Boundary Harnack principle and decay estimates for p-harmonic functions. special session on Subelliptic PDEs and Sub-Riemannian Geometry, AMS Sectional meeting, Fayetteville, Arkansas.
(08-2006). On covering theorems and Hardy-Littlewood maximal functions. Ramanujan Institute of Mathematical Sciences, Chennai University, Chennai, India.
(08-2006). A series of 5 lectures on Sobolev space theory, fine regularity, and non-linear potential theory. Indian Institute of Technology at Madras, Chennai, India.
(05-2005). On conformal Martin boundaries of domains in metric measure spaces. Analysis seminar, University of Helsinki, Finland.
(05-2005). Conformal Martin boundary of Euclidean domains. Analysis seminar, University of Link¨oping, Sweden.
(02-2005). On equivalence of Dirichlet forms and Newtonian spaces. Analysis seminar, University of Michigan, Ann Arbor.
(08-2004). Dirichlet forms and Newton-Sobolev spaces for metric spaces supporting Poincar´e inequalities. International Workshop on Potential Theory, Matsue, Japan.
(07-2004). Domar’s argument and a proof of Carleson estimates for p-quasiminimizers. conference on analysis on metric spaces at the Banach center, Poland.
(07-2004). Introduction to Dirichlet forms on metric spaces. analysis seminar, Helsinki University of Technology, Finland.
(04-2004). Domar’s argument in the non-linear setting. analysis seminar, University of Kentucky, Lexington.
(10-2003). Lipschitz regularity of Cheeger–harmonic functions in metric spaces. AMS sectional meeting, Boulder, CO.
(07-2003). An introduction to the Dirichlet problem for p-harmonic functions. Banff International Research Station, Banff, Canada.
(06-2003). Analysis on metric spaces. analysis seminar, Link¨oping University, Sweden.
(06-2003). Conformal Martin boundary; construction and properties. 19th Rolf Nevanlinna Colloquium, University of Jyv¨askyl¨a, Finland.
(11-2002). Perron method for the p–Laplacian on domains in metric spaces. Analysis seminar talk, University of Illinois at Urbana-Champaign.
(04-2002). Conformal Martin boundary of domains in metric measure spaces. University of Arkansas.
(10-2001). Potential theoretic measures on boundaries of domains in metric spaces. Special session on geometric function theory, AMS sectional meeting, Chattanooga, TN.
(04-2001). Dirichlet forms on metric spaces. Conference in honor of Olli Martio, University of Jyv¨askyl¨a.
(03-2001). Self-improvement of uniform p-fatness for metric spaces, Special session on geometric analysis. AMS sectional meeting, University of Kansas at Lawrence, KS.
(11-2000). On p-singular Functions and p-hyperbolicity. SUNY(Stony Brook) and Wesleyan University
(04-2000). On Harmonic Functions on Metric Spaces. University College Dublin
(10-1999). p-harmonic functions on metric spaces, Special session on geometric function theory. AMS sectional meeting, Charlotte, NC.
(02-1998). On Newtonian Spaces. University of Jyv¨askyl¨a and University of Helsinki
