PUBLICATIONS of David A Herron

  1. The Harnack and other conformally invariant metrics, Kodai Mathematical Journal, Vol. 10, No. 1 (1987) 9-19.
  2. The geometry of uniform, quasicircle, and circle domains, Annales Academiae Scientiarum Fennicae, Series A I Mathematica, Vol. 12 (1987) 217-228.
  3. The interior distance ratio in quadrilaterals and inequalities for rings (with Bruce Hanson), Complex Variables: Theory and Application, Vol. 9 (1988) 321-325.
  4. Positive harmonic functions in admissible and uniform domains (with Matti Vuorinen), International Journal of Analysis and its Applications, Vol. 8 (1988) 187-206.
  5. Metric boundary conditions for plane domains, Complex Analysis, Proceedings of the 13th Rolf Nevanlinna Colloquium in Joensuu, Finland, August 10-13, 1987, Lecture Notes in Mathematics, No. 1351, Springer-Verlag, Berlin (1988) 193-200. (refereed)
  6. Uniform domains: sufficient conditions, Bounded mean oscillation in complex analysis, Proceedings of Rolf Nevanlinna Institute's BMO Seminar in Joensuu, Finland, August 17-20, 1987, University of Joensuu, Publications in Sciences (1989) 57-69. (refereed)
  7. Positive harmonic functions and complete metrics (with Joel L. Schiff), Canadian Mathematical Bulletin, Vol. 32 (3) (1989) 286-297.
  8. Ring domains with separating circles or separating annuli(with Xiangyang Liu and David Minda), Journal d'Analyse Mathématique, Vol. 53 (1989) 233-252.
  9. Quasiextremal distance domains and conformal mappings onto circle domains (with Pekka Koskela), Complex Variables: Theory and Application, Vol. 15 (1990) 167-179.
  10. Uniform, Sobolev extension and quasiconformal circle domains (with Pekka Koskela), Journal d'Analyse Mathématique, Vol. 57 (1991) 172-202.
  11. Uniform and Sobolev extension domains (with Pekka Koskela), Proceedings American Math. Society, Vol. 114, No. 2 (1992) 483-489.
  12. Locally uniform domains and quasiconformal mappings (with Pekka Koskela), Annales Academiae Scientiarum Fennicae, Series A I Mathematica, Vol. 20 (1995) 187-206.
  13. Poincaré domains and quasiconformal homeomorphisms (with Pekka Koskela), Siberian Mathematical Journal, Vol. 36 (6) (1995) 1416-1434.
  14. Conformal capacity and the quasihyperbolic metric (with Pekka Koskela), Indiana University Mathematics Journal, Vol. 45 (1996) 333-359.
  15. Continuity of Sobolev functions and Dirichlet finite harmonic measures (with Pekka Koskela), Potential Analysis, Vol. 6 (1997) 347-353.
  16. Higher dimensional Ahlfors regular sets and chordarc curves in tex2html_wrap_inline94 (with Manouchehr Ghamsari), Rocky Mountain Journal of Mathematics, Vol. 28, No. 1 (1998) 191-222.
  17. Uniform estimates for the hyperbolic metric and Euclidean distance to the boundary (with Barbara Brown Flinn), Michigan Mathematical Journal, Vol. 46, No. 1 (1999) 13-27.
  18. Bilipschitz homogeneous Jordan curves (with Manouchehr Ghamsari), Transactions American Mathematical Society, Vol. 351 No. 8 (1999) 3197-3216.
  19. John domains and the quasihyperbolic metric, Complex Variables: Theory and Applications, Complex Variables: Theory and Application, Vol. 39 (1999) 327-334.
  20. Bilipschitz group actions and homogeneous Jordan curves (with Volker Mayer), Illinois Journal of Mathematics, Vol. 43, No. 4 (1999) 770-792.
  21. Ahlfors three-point condition, Complex Variables: Theory and Applications, Vol. 41 (2000) 327-329.
  22. Comparing invariant distances and conformal metrics on Riemann Surfaces (with David Minda), Israel Journal of Mathematics, Vol. 122 (2001) 207-220.
  23. Fractal inner chordarc disks, (with Terry Sullivan) Journal d'Analyse Mathématique, Vol. 84 (2001) 173-205.
  24. Quasiextremal distance sets, (with Shanshuang Yang), Analysis, Vol. 23 (2003) 27-50.
  25. Mappings of finite distortion: gauge dimension of generalized quasispheres (with Pekka Koskela), Illinois Journal Mathematics, Vol. 47 (2003) 1243-1259.
  26. A Möbius invariant metric for regions on the Riemann sphere (with William Ma and David Minda), Reports University Jyväskylä, Vol. 92 (2003), 101-118.
  27. Conformal deformations of uniform Loewner spaces, Mathematics Proceedings of Cambridge Philosphical Society, Vol. 136 (2004) 325-360.
  28. Estimates for conformal metric ratios (with William Ma and David Minda), Computational Methods and Function Theory, Vol. 5, No. 2 (2005) 323-345.
  29. Quasiconformal deformations and volume growth, Proceedings of London Mathematical Society, Vol. 92, No. 3 (2006) 161-199.
  30. Uniform spaces and Gromov hyperbolicity, Quasiconformal Mappings and their Applications, Narosa, New Delhi, India (2007) 79-115.
  31. Uniform domains and capacity (with Stephen Buckley), Israel Journal of Mathematical, Vol. 158 (2007), 129-157.
  32. Uniform spaces and weak slice spaces (with Stephen Buckley), Conformal Geometry and Dynamics, Vol. 11 (2007), 191-206.
  33. Geodesics and curvature of Möbius invariant metrics (with Zair Ibragimov and David Minda), Rocky Mountain Journal of Mathematics, Vol. 38, No. 3 (2008), 891-921.
  34. Metric space inversions, quasihyperbolic distance and uniform spaces (with Stephen Buckley and Xiangdong Xie), Indiana University Mathematics Journal, Vol. 57, No. 2 (2008), 837-890.
  35. Quasiconvex domains in Euclidean space (with Hrant Hakobyan), Annales Academiae Scientiarum Fennicae, Vol. 33 (2008) 205-230.
  36. Möbius invariant metrics biLipschitz equivalent to the hyperbolic metric (with William Ma and David Minda), Conformal Geometry and Dynamics, Vol. 12 (2008) 67-96.
  37. Uniformity from Gromov hyperbolicity (with Nageswari Shanmugalingham and Xiangdong Xie), Illinois Journal of Mathematics, Vol. 52, No. 4 (2008) (published in November 2009) 1065-1109.
  38. Bilipschitz homogeneity and inner diameter distance (with David Freeman), Journal d'Analyse Mathématique, Vol. 111 (2010) 1-46.
  39. Geometry and topology of intrinsic distances, J. Analysis, Vol. 18 (2010) 197-231.
  40. Uniform metric spaces, annular quasiconvexity and pointed tangent spaces, Mathematica Scandinavica, Vol. 108, No. 1 (2011) 115-145.

ARTICLES ACCEPTED FOR PUBLICATION

41.
Quasicircles and bounded turning circles modulo bilipschitz maps (with Daniel Meyer), Revista Matemática Iberoamericana, to appear (accepted September 2010), 30 pages.
42.
Riemann Maps and Diameter Distance, American Mathematical Monthly, to appear (accepted February 2011), 9 pages.

PREPRINTS

43.
Homeomorphisms of annuli, Dirichlet energy and mean distortion (with Gaven Martin), in preparation, currently 20 pages.
44.
Gromov-Hausdorff convergence of pointed metric spaces, in preparation, currently 31 pages.
45.
Mappings of Finite Distortion: Modulus of Continuity and Compression of Hausdorff Measure (with Albert Clop), in preparation, currently 27 pages.
Quasiconformal homeomorphisms, uniform domains and Sobolev extension domains, lecture notes for colloquia talks.
Reflections across circles, lecture notes for undergraduate talks.