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David A Herron
Professor
810D Old Chemistry Building
513-556-4075
david.a.herron@uc.edu
http://math.uc.edu/~herron
Education
PhD, University of Michigan, 1984.
Peer Reviewed Publications
Herron, D., Ibragimov, Z., & Minda, D. (2008). Geodesics and curvature of Mobius invariant metrics. Rocky Mountain Journal of Mathematics, 38(3), 891-921.
Buckley, S., Herron, D., & Xiangdong, X. (2008). Metric space inversions, quasihyperbolic distance and uniform spaces. Indiana University Mathematics Journal, 57(2), 837-890.
Hakobyan, H., & Herron, D. (2008). Annales Academiae Scientiarum Fennicae. 33, 205-230.
Herron, D., Ma, W., & Minda, D. (2008). Mobius invariant metrics biLipschitz equivalent to the hyperbolic metric. 12, 67-96.
Herron, David (2007). Uniform spaces and Gromov hyperbolicity. Quasiconformal Mappings and their Applications 79-115.
Buckley, S., & Herron, D. (2007). Uniform domains and capacity. Israel Journal of Mathematical, 158, 129-157.
Buckley, S., & Herron, D. (2007). Uniform spaces and weak slice spaces. Conformal Geometry and Dynamics, 11, 191-206.
Herron, David (2006). Quasiconformal deformations and volume growth. Proceedings of London Mathematical Society, 92(3), 161-199.
Herron, David, Ma, William, & Minda, David (2005). Estimates for conformal metric ratios. Computational Methods and Function Theory, 5(2), 323-345.
Herron, David (2004). Conformal deformations of uniform Loewner spaces. Mathematics Proceedings of Cambridge Philosophical Society, 136, 325-360.
Herron, David, & Yang, Shanshuang (2003). Quasiextremal distance sets. Analysis, 23, 27-50.
Herron, David, & Koskela, Pekka (2003). Mappings of finite distortion: gauge dimension of generalized quasispheres. Illinois Journal Mathematics, 47, 1243-1259.
Herron, David, Ma, William, & Minda, David (2003). A M¨obius invariant metric for regions on the Riemann sphere. Reports University Jyv¨askyl¨a, 92, 101-118.
Herron, David, & Minda, David (2001). Comparing invariant distances and conformal metrics on Riemann Surfaces. Israel Journal of Mathematics, 122, 207-220.
Herron, David, & Sullivan, Terry (2001). Fractal inner chordarc disks. Journal d’Analyse Math´ematique, 84, 173-205.
Herron, David, & (2000). Ahlfors three-point condition. Complex Variables: Theory and Applications, 41, 327-329.
Herron, David, & Flinn, Barbara (1999). Uniform estimates for the hyperbolic metric and Euclidean distance to the boundary. Michigan Mathematical Journal, 46(1), 13-27.
Herron, David, & Ghamsari, Manouchehr (1999). Bilipschitz homogeneous Jordan curves. Transactions American Mathematical Society, 351(8), 3197-3216.
Herron, David (1999). John domains and the quasihyperbolic metric. Complex Variables: Theory and Applications, 39, 327-334.
Herron, David, & Mayer, Volker (1999). Bilipschitz group actions and homogeneous Jordan curves. Illinois Journal of Mathematics, 43(4), 770-792.
Herron, David, & Ghamsari, Manouchehr (1998). Higher dimensional Ahlfors regular sets and chordarc curves in Rn. Rocky Mountain Journal of Mathematics, 28(1), 191-222.
Herron, David, & Koskela, Pekka (1997). Continuity of Sobolev functions and Dirichlet finite harmonic measures. Potential Analysis, 6, 347-353.
Herron, David, & Koskela, Pekka (1996). Conformal capacity and the quasihyperbolic metric. Indiana University Mathematics Journal, 45, 333-359.
Herron, David, & Koskela, Pekka (1995). Locally uniform domains and quasiconformal mappings. Annales Academiae Scientiarum Fennicae, Series A I Mathematica, 20, 187-206.
Herron, David, & Koskela, Pekka (1995). Poincar´e domains and quasiconformal homeomorphisms. Siberian Mathematical Journal, 36(6), 1416-1434.
Herron, David, & Koskela, Pekka (1992). Uniform and Sobolev extension domains. Proceedings American Math. Society, 114(2), 483-489.
Herron, David, & Koskela, Pekka (1991). Uniform, Sobolev extension and quasiconformal circle domains. Journal d’Analyse Math´ematique, 57, 172-202.
Herron, David, & Koskela, Pekka (1990). Quasiextremal distance domains and conformal mappings onto circle domains. Complex Variables: Theory and Application, 15, 167-179.
Herron, David, & Schiff, Joel L. (1989). Positive harmonic functions and complete metrics. Canadian Mathematical Bulletin, 32(3), 286-297.
Herron, David, Liu, Xiangyang, & Minda, David (1989). Ring domains with separating circles or separating annuli. Journal d’Analyse Math´ematique, 53, 233-252.
Hanson, Bruce, & Herron, David (1988). The interior distance ratio in quadrilaterals and inequalities for rings. Complex Variables: Theory and Application, 9, 321-325.
Herron, David, & Vuorinen, Matti (1988). Positive harmonic functions in admissible and uniform domains. International Journal of Analysis and its Applications, 8, 187-206.
Herron, David (1987). The Harnack and other conformally invariant metrics. Kodai Mathematical Journal, 10(1), 9-19.
Herron, David (1987). The geometry of uniform, quasicircle, and circle domains. Annales Academiae Scientiarum Fennicae, Series A I Mathematica, 12, 217-228.
Herron, D., Shanmugalingham, N., & Xiangdong, X. Uniformity from Gromov hyperbolicity. Illinois Journal of Mathematics 35 pages.
Freeman, D., & Herron, D. BiLipschitz homogeneity and inner diameter distance. Journal d'Analyse Mathematique 34 pages.
Other Publications
(2007). Uniform spaces and Gromov hyperbolicity. Quasiconformal Mappings and their Applications Narosa 79-115. New Delhi, India.
(1987). Metric boundary conditions for plane domains. Complex Analysis, Proceedings of the 13th Rolf (1351), 193-200. Joensuu, Finland: Springer-Verlag, Berlin.
(1987). Uniform domains: sufficient conditions, Bounded mean oscillation in complex analysis. Proceedings of Rolf Nevanlinna Institute’s BMO Seminar 57-69. Joensuu, Finland.
Lectures
(06-2007). Joint Summer Conference. University of Manitoba, Winnipeg, Manitoba, CA.
(03/16/2007). Euclidean QuasiConvexity. Miami University.
(10/21/2006). Quasiconvex Plane Domains. University of Cincinnati.
(09/29/2006). Metric Space Inversions. Virginia Polytechnic University.
(07/14/2006). Metric Space Inversions and Quasihyperbolic Geometry. Conference on Geometric Analysis and Applications, University of Illinois, Urbana-Champaign, IL.
(01/03/2006). Uniform Spaces, Gromov Hyperbolicity, Capacity, and Slice Conditions. International Conference on Geometric Function Theory, Special Functions and their Applications, Forum d’Analyste, Pondicherry, India.
(12/28/2005). Uniform Spaces and Gromov Hyperbolicity. International Workshop on Quasiconformal Mappings and their Applications, Indian Institute of Technology (Madras) Chennai, India.
(07/20/2004). Quasiconformal deformations and volume growth. Analysis on Metric Measure Spaces, Polish Academy of Sciences Institute of Mathematics, Bedlewo, Poland.
(12/04/2003). Uniformization, hyperbolicity and volume growth. Wesleyan University.
(10/03/2003). Conformal deformations and volume growth. University of Colorado, Boulder.
(12/02/2002). Fractal function theory. ‘What’s Up Doc?’ Seminar, University of Cincinnati .
(10/05/2001). Conformal deformations of uniformizable spaces. University of Tennessee, Chattanooga.
(03/09/2001). Fractal inner chordarc disks. University of Helsinki.
(02/14/2001). Conformal deformations of uniformizable spaces. University of Jyv¨askyl¨a.
(11/28/2000). The hyperbolic/quasihyperbolic metric ratio. University of Michigan.
(10/25/2000). Inner chordarc disks. University of Michigan.
Paper Presentations
Conformal deformations and volume growth. University of Colorado, Boulder. 2003.
