Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, Illinois 61801-2975
Office: 236 Illini Hall
Phone: (217) 244-7297
Fax: (217) 333-9576
Area of interest and specialization:
Geometric and Complex Analysis, Potential Theory and Related Problems in Probability and Partial Differential Equations
- (with D. Ntalampekos) Non-Removability of Sierpinski Spaces. (pdf)
- (with P. Pankka) Deformation and Quasiregular Extension of Cubical Alexander Maps. (pdf) (slide)
- (with J. Llorente, J. Manfredi, and W. Troy) On p-Harmonic Measures in Half Spaces. (pdf)
- Geometry of Grushin spaces, Illinois J. Math. 59 (2015), no. 1, 21–41. (pdf)
- (with V. Vellis) Quasisymmetric spheres over Jordan domains, Trans. Amer. Math. Soc. 368 (2016), no. 8, 5727–5751. (pdf)
- (with A. Fletcher) Julia Sets and Wild Cantor Sets, Geometriae Dedicata, Geometriae Dedicata (2015) 174:169-176. (pdf)
- BiLipschitz embedding of Grushin plane in R^3. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 2, 633–644. (pdf)
- (with Pekka Pankka and Kai Rajala) Quasiregular ellipticity of open and generalized manifolds, Computational Methods and Function Theory, Gehring Memorial Volume, 14 (2014), Issue 2-3, 383-398. (pdf)
- (with V. Vellis), Sets of constant distance from a Jordan curve. Ann. Acad. Sci. Fennicae Math, 39 (2014) no.1, 211 - 230. (pdf)
- (with P. Pankka), Geometry and Quasisymmetic Parametrization of Semmes Spaces. Revista Mat. Iberoamericana, 30 (2014), no.3, 893-960. (pdf)
- (with R. Kangaslampi and K. Peltonen), Uniformly Quasiregular Maps with Toroidal Julia Sets. Conformal Geometry and Dynamics 16 (2012), 81-88. (pdf)
- Semmes Spaces, appeared in All That Math -- Portraits of Mathematicians as Young Readers, Revista Mathematica Iberoamericana, 2011. (pdf)
- (with J. Heinonen) Quasisymmetric nonparametrization and spaces associated with the Whitehead continuum. Geometry and Topology 14 (2010), no. 2, 773-798. (pdf)
- (with L.V. Kovalev and D. Maldonado), Doubling Measures, Monotonicity, and Quasiconformality. Mathematische Zeitschrift 257 (2007), no. 3, 525-545. (pdf)
- Doob's Contribution to Function Theory. Illinois J. Math. 50 (2006), no. 1-4, 1019-1028. (pdf)
- (with J.G. Llorente and J. Manfredi), p-Harmonic measure is not subadditive. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), no. 2, 357-373. (pdf)
- (with R. Kaufman and J.T. Tyson), Smooth quasiregular maps with branching in Rn. Publ. Math. IHES, No. 101 (2005), 209-241. (pdf)
- (with J.T. Tyson), Characterizations of snowflake metric spaces. Ann. Acad. Sci. Fennicae Math. 30 (2005), no. 2, 313-336. (pdf)
- (with J. Tyson), Quasiconformal dimensions of self-similar sets. Revista Mat. Iberoamericana, 22 (2006), no. 1, 205-258. (pdf)
- (with R. Kaufman and J.G. Llorente), Nonlinear harmonic measures on trees. Ann. Acad. Sci. Fennicae Math. 28 (2003) 279-302. (pdf)
- Symmetric stable processes stay in thick sets. Ann. Probability 32 (2004) 315-336. (pdf)
- (with D. Drasin), The sharpness of a criterion of MacLane for the Class A. J. London Math. Soc. (2) 67 (2003) 433-447. (pdf)
- Harmonic measures for symmetric stable processes. Studia Math. 149 (2002) 281-293.(pdf)
- (with R. Kaufman), Fatou theorem of p-harmonic functions on trees. Ann. Probab 28 (2000) 1138-1148. (pdf)
- (with R.M. Song), Boundary Harnack principle for symmetric stable processes. J. Funct. Anal. 168 (1999) 403-427. (pdf)
- (with R.B. Sowers), Thermal capacity estimates on the Allen-Cahn equation. Trans. Amer. Math. Soc. 351 (1999) 2553-2567.
- Growth and asymptotic sets of subharmonic functions. II. Publ. Mat. 42 (1998) 449-460.
- Removability of sets for quasiconformal mappings and Sobolev spaces. Complex Variables Theory Appl. 37 (1998) 491-506.
- Growth and asymptotic sets of subharmonic functions. J. London Math. Soc. (2) 58 (1998) 656-668.
- Hausdorff dimension and doubling measures on metric spaces. Proc. Amer. Math. Soc. 126 (1998) 1453-1459.
- Doubling measures with different bases. Colloq. Math. 76 (1998) 49--55.
- (with R. Kaufman), On removable sets for quasiconformal mappings. Ark. Mat. 34 (1996) 141-158.
- Harmonic measures for elliptic equations of nondivergence form. Potential Anal. 5 (1996) 45-59.
- (with R. Kaufman) Two problems on doubling measures, Rev. Mat. Iberoamericana, 11 (1995), no. 3, 527-545. (pdf)
- (with L. Lewis) On conjectures of Arakelyan and Littlewood, Jour. d'Analyse Math., 50 (1988), 259 - 283. (pdf)
- (with R. Kaufman) Parabolic Potential Theory, J. Differential Equations 43 (1982), no.2, 204 -234. (pdf)
- (with W. Hayman) Level sets of univalent functions, Comment. Math. Helvetici, 56 (1981), 366 - 403. (pdf)
Last modified March 13, 2019