Expert Profile: David Herron | Research Directory

Education

PhD: University of Michigan Ann Arbor, Michigan, 1984 (Mathematics)

BS (with High Honors): University of Delaware Newark, Delaware, 1977 (Mathematics)

Research and Practice Interests

Geometric analysis, analysis in metric spaces, geometric function theory, quasiconformal mappings, conformal geometry, hyperbolic geometry, potential theory, complex analysis

Positions and Work Experience

1999 -To Present Professor, University of Cincinnati, Cincinnati, Ohio

2004 -2006 Graduate Program Director, University of Cincinnati, Cincinnati, Ohio

1991 -1999 Associate Professor, University of Cincinnati, Cincinnati, Ohio

1985 -1991 Assistant Professor, University of Cincinnati, Cincinnati, Ohio

1984 -1985 Assistant Professor, University of California, Los Angeles, California

05-2009 -07-2009 Visiting Professor, Massey University, Albany, New Zealand

01-2009 -02-2009 Visiting Professor, University of Jyväskylä, Jyväskylä, Finland

01-2001 -03-2001 Visiting Professor, University of Jyväskylä, Jyväskylä, Finland

06-1990 -07-1990 Visiting Professor, University of Jyväskylä, Jyväskylä, Finland

05-1998 -05-1998 Visiting Professor, Université de Lille, Lille, France

05-1990 -05-1990 Visitor, Mittag-Leffler Institute, Djursholm, Sweden

09-2000 -12-2000 Visiting Scholar, University of Michigan, Ann Arbor, Michigan

09-1992 -06-1993 Visiting Scholar, University of Michigan, Ann Arbor, Michigan

09-1991 -09-1991 Visiting Scholar, University of Michigan, Ann Arbor, Michigan

06-1988 -06-1988 Visiting Scholar, University of Michigan, Ann Arbor, Michigan

1977 -1984 Teaching Assistant, University of Michigan, Ann Arbor, Michigan

06-1978 -09-1978 Programmer, University of Princeton Plasma Physics Lab, Princeton, NJ

06-1977 -09-1977 Programmer, University of Princeton Plasma Physics Lab, Princeton, NJ

06-1976 -09-1976 Programmer, University of Princeton Plasma Physics Lab, Princeton, NJ

Research Support

Grant: #DMS-1317141 Investigators:Herron, David 07-15-2013 -06-30-2014 National Science Foundation Rolf Nevanlinna Colloquium 2013 Role:PI $49,921.00 Active Level:Federal

06-2012 -08-2012 Charles Phelps Taft Memorial Fund Role:PI $8000 Completed Type:Fellowship Level:University

Grant: #INT-0226822 Investigators:Herron, David 02-01-2003 -01-31-2004 National Science Foundation Future Trends in Geometric Function Theory Role:PI $22,000.00 Closed Level:Federal

Grant: #DMS-1500454 Investigators:Herron, David 03-01-2015 -02-29-2016 National Science Foundation Modern Aspects of Complex Geometry Role:PI $49,935.00 Awarded Level:Federal

Abbreviated Publications

Peer Reviewed Publications

Sorry about the mess below....bad software :-((

Mappings of Finite Distortion in $\mathsf{L}^p_{\rm loc}$ : Modulus of Continuity and Compression of Hausdorff Measure: \textsf{Israel Journal of Mathematics}, Vol.\ \textbf{200}, (2014) 225--250.

Universal convexity for quasihyperbolic type metrics, \textsf{Conformal Geometry and Dynamics}, Vol.\ \textbf{20} (2016) 1--24.

Ferrand's M\"obius invariant metric (with Poranee Julian), \textsf{Journal of Analysis}, Vol.\ \textbf{21}, (2013), 101--121.

Riemann Maps and Diameter Distance, American Mathematical Monthly, Vol. 119, No. 2, (2012) 140–147.

Mappings with Subexponentially Integrable Distortion: Modulus of Continuity, and Distortion of Hausdorff Measure and Minkowski Content, (with Albert Clop), \textsf{Illinois Journal of Mathematics}, Vol.\ \textbf{57}, no.\ 4, (2013) 965--1008

Quasicircles and bounded turning circles modulo bilipschitz maps (with Daniel Meyer), Revista Matemática Iberoamericana, Vol. 28, no. 3 (2012) 603–630.

Geometry and topology of intrinsic distances, Journal of Analysis, Vol. 18 (2010) 197-231.

Uniform metric spaces, annular quasiconvexity and pointed tangent spaces, Mathematica Scandinavica, Vol. 108, No. 1 (2011) 115-145.

Bilipschitz homogeneity and inner diameter distance (with David Freeman), Journal d'Analyse Mathématique, Vol. 111 (2010) 1-46.

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.

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.

Quasiconvex domains in Euclidean space (with Hrant Hakobyan), Annales Academiae Scientiarum Fennicae, Vol. 33 (2008) 205-230.

Möbius invariant metrics biLipschitz equivalent to the hyperbolic metric (with William Ma and David Minda), Conformal Geometry and Dynamics, Vol. 12 (2008) 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.

(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.

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.

Under Review

Quasiconvexity in the Heisenberg group (with A. Lukyanenko and J.T. Tyson)

In Press

Gromov-Hausdorff distance for pointed metric spaces, to appear in \textsf{Journal of Analysis} in 2016.

Blashke's rolling ball property and conformal metric ratios (with Poranee Julian), to appear in \textsf{Rocky Mountain Journal of Mathematics} in 2016.

Work in Progress

Homeomorphisms of annuli, Dirichlet energy and mean distortion (with Gaven Martin)

Quasi-hyperbolic geodesics are hyperbolic quasi-geodesics

Quasihyperbolic universal convexity of balls

Presentations

Invited Presentations

(03-10-2012. ) Hausdorff Measure and Mappings of Finite Distortion, .American Mathematical Society Meeting #1079, University of South Florida, Tampa, FL. Professional Meeting. . Level:Regional

Lecture

(06-2007. ) Joint Summer Conference .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 .

(07-14-2006. ) Metric Space Inversions and Quasihyperbolic Geometry .University of Illinois, Urbana-Champaign, IL.

(01-03-2006. ) Uniform Spaces, Gromov Hyperbolicity, Capacity, and Slice Conditions .Forum d’Analyste, Pondicherry, India.

(12-28-2005. ) Uniform Spaces and Gromov Hyperbolicity .Indian Institute of Technology (Madras) Chennai, India.

(07-20-2004. ) Quasiconformal deformations and volume growth .Polish Academy of Sciences Institute of Mathematics, Bedlewo, Poland.

(12-04-2003. ) Uniformization, hyperbolicity and volume growth .

(10-03-2003. ) Conformal deformations and volume growth .Boulder.

(12-02-2002. ) Fractal function theory .University of Cincinnati .

(10-05-2001. ) Conformal deformations of uniformizable spaces .Chattanooga.

(03-09-2001. ) Fractal inner chordarc disks .

(02-14-2001. ) Conformal deformations of uniformizable spaces .

(11-28-2000. ) The hyperbolic/quasihyperbolic metric ratio .University of Michigan.

(10-25-2000. ) Inner chordarc disks .University of Michigan.

Paper Presentations

(2003. ) Conformal deformations and volume growth .University of Colorado, Boulder.

Event Organized

Geometric Mapping Theory in Euclidean and Non-Euclidean Spaces

Geometric Mapping Theory in Euclidean and Non-Euclidean Spaces Conference 03-12-2011 03-13-2011 Southern Georgia University, Statesboro, GA Level:Regional

Funding for RNC2013

Funding for RNC2013 Conference 05-2013 09-2013 Helsinki, Finland Level:International

Service

Taft Research Center (Taft Travel Committee ) Committee Member Type:University/College Service Level:College 09-2010 -08-2011

Taft Research Center (Taft Travel Committee ) Committee Member Type:University/College Service Level:University 01-2011 -03-2011

University Taft Research Center (Taft Travel Committee ) Committee Member Type:University/College Service Level:College 03-2011 -06-2011

University Taft Research Center (Taft ExecutiveCommittee ) Committee Member Type:University/College Service Level:College 09-2011 -08-2012

Department of Mathematical Sciences (RPT Committee ) Elected Member Type:Departmental Service Level:Department 09-2009 -06-2012

Department of Mathematical Sciences (Topology Preliminary Examination ) Committee Chair Type:Departmental Service Level:Department 09-2010 -10-2011

Department of Mathematical Sciences (Topology Preliminary Examination ) Committee Chair Type:Departmental Service Level:Department 09-2009 -10-2011

Department of Mathematical Sciences (Topology Preliminary Examination ) Committee Chair Type:Departmental Service Level:Department 09-2010 -10-2011

Department of Mathematical Sciences (Merit Grievance Committee ) Elected Member Type:Departmental Service Level:Department 01-2011 -To Present

Department of Mathematical Sciences (Graduate Advising ) Other Type:Departmental Service Level:Department 09-2011 -06-2012

Department of Mathematical Sciences (Mentor to Junior Faculty ) Mentor Type:Departmental Service Level:Department 01-2011 -06-2012

Department of Mathematical Sciences (RPT Committee ) Elected Member Type:Departmental Service Level:Department 09-2009 -06-2012

Department of Mathematical Sciences (Text Book Selection Committee ) Committee Member Type:Departmental Service Level:Department 01-2011 -06-2011

Department of Mathematical Sciences (Text Book Selection Committee ) Committee Member Type:Departmental Service Level:Department 01-2011 -06-2012

Journal of Geometric Analysis Peer Review/Referee Type:Editorial Service Level:International 02-2012 -05-2012

Annales Scientifiques de l’´Ecole Normale Sup´erieure Peer Review/Referee Type:Editorial Service Level:International 08-2012 -10-2012

Journal of Mathematical Analysis and Applications Peer Review/Referee Type:Editorial Service Level:International 10-2012 -12-2012

The Royal Society of Edinburgh: Proceedings Peer Review/Referee Type:Editorial Service Level:International 10-2012 -12-2012

Charles Phelps Taft Research Center (Taft Executive Committee ) Committee Member Type:University/College Service Level:University 01-2012 -06-2012

(RPT ) Committee Member Type:Departmental Service Level:Department 01-2012 -06-2012

(Topology Prelim ) Committee Member Type:Departmental Service Level:Department 05-2012 -08-2012

(Complex Analysis Prelim ) Committee Member Type:Departmental Service Level:Department 05-2012 -06-2012

(Qualifying Exam Committee ) Committee Chair Type:Departmental Service Level:Department 03-2012 -09-2012

(Linear Algebra Textbook Selection ) Committee Member Type:Departmental Service Level:Department 03-2012 -05-2012

Mentor Type:Departmental Service Level:Department 08-2012 -12-2012

Graduate Advisor Type:Departmental Service Level:Department 01-01-2013 -12-31-2013

(Graduate Affairs Committee ) Committee Member Type:Departmental Service Level:Department BAD DATE

(Graduate Affairs Committee ) Committee Member Type:Departmental Service Level:Department 03-01-2013 -07-31-2013

(Graduate Affairs Committee ) Committee Member Type:Departmental Service Level:Department 05-01-2013 -07-31-2013

(Graduate Affairs Committee ) Committee Member Type:Departmental Service Level:Department 08-01-2013 -12-31-2013

(VAP Search Committee ) Type:Departmental Service Level:University 03-01-2013 -07-31-2013

(Qualifying Exam Committee ) Committee Chair Type:Departmental Service Level:Department 01-01-2013 -12-31-2013

The Royal Society of Edinburgh: Proceedings A Peer Review/Referee Type:Editorial Service Level:International

Journal of Mathematical Analysis and Applications Peer Review/Referee Type:Editorial Service Level:International

Tohoku Mathematical Journal Peer Review/Referee Type:Editorial Service Level:International

(Annales Scientifiques de l’ ´Ecole Normale Sup´erieure ) Peer Review/Referee Type:Editorial Service Level:International

Real Analysis Exchange Peer Review/Referee Type:Editorial Service Level:International

Journal d’Analyse Math´ematique Peer Review/Referee Type:Editorial Service Level:International

Keywords

geometric function theory, quasiconformal mappings, geometric analysis, analysis in metric spaces

Professional Affiliation

1977 -To Present: Mathematical Association of America

1979 -To Present: American Mathematical Society

1990 -To Present: Finnish Mathematical Society

1987 -2003: American Association of University Professors

Courses Taught

15-MATH-604 GENERAL TOPOLOGY Differential Topology Level:Graduate

15-MATH-604 GENERAL TOPOLOGY Algebraic Topology Level:Graduate

Advanced Calculus I Level:Graduate

15-MATH-352 LINEAR ALGEBRA II Level:Undergraduate

15-MATH-273 DIFFERENTIAL EQNS Level:Undergraduate

Linear Algebra Level:Undergraduate

15-MATH-351 LINEAR ALGEBRA I Level:Undergraduate

15-MATH-264 CALC & AN GEOM IV Level:Undergraduate