Publications

1. Schippers, Eric.  The Calculus of conformal metrics and univalence criteria for holomorphic functions.  Thesis. June 1999, University of Toronto.

2. Schippers, Eric.  Distortion theorems for higher order Schwarzian derivatives of univalent functions. Proc. Amer. Math. Soc. 128 (2000), no. 11, 3241--3249.

3. Schippers, Eric.  Conformal invariants and higher-order Schwarz lemmas . J. Anal. Math. 90 (2003), 217--241.

4. Schippers, Eric.  Estimates on kernel functions of elliptically Schlicht domains . Comput. Methods Funct. Theory 2 (2002), no. 2, 579--596.

5. Schippers, Eric.  Conformal invariants corresponding to pairs of domains. Future trends in geometric function theory, (Conf. Proc.) 207--219, Rep. Univ. Jyväskylä Dep. Math. Stat. 92 Univ. Jyväskylä, Jyväskylä (2003). 

6. Schippers, Eric.  Behaviour of kernel functions under homotopic variations of planar domains.   Comput. Methods Funct. Theory 4 (2004), no. 2, 283--298. 

7. Radnell, David; and Schippers, Eric.  Quasisymmetric sewing in rigged Teichmueller space,   Communications in Contemporary Mathematics 8 (2006) no. 4, 481--534.

8. Schippers, Eric.  The Power matrix, coadjoint action and quadratic differentials.   J. Anal. Math. 98 (2006), 249--278.

9. Radnell, David; and Schippers, Eric.  A complex structure on the moduli space of rigged Riemann surfacesJournal of Geometry and Symmetry in Physics 5 (2006), 82--94.

10. Schippers, Eric.  The calculus of conformal metricsAnnal. Acad. Scient. Fenn.  32 (2007), 497--521.

11. Roth, Oliver; and Schippers, Eric.  The Loewner and Hadamard variations.  with O. Roth, Illinois J. Math 52 no. 4 (2008) 1399--1415.

12. Schippers, Eric; and Staubach, Wulf.  Variation of Neumann and Green functions under homotopies of the boundary. with W. Staubach, Israel J. Math. 173 no 1, (2009), 279--303. 

13.  Radnell, David; and Schippers, Eric.   A complex structure on the set of quasiconformally extendible mappings into a Riemann surface.  J. Anal. Math. 108 no. 1 (2009)  277--291.

14. Radnell, David; and Schippers, Eric.  Fiber structure and local coordinates for the Teichmueller space of a bordered Riemann surface.  Conformal Geometry and Dynamics 14 (2010), 14--34arxiv version.

15. Schippers, Eric.  A power matrix approach to the Witt algebra and Loewner equationsComputational Methods and Function Theory 10 (2010) no 1, 399--420.

16. Schippers, Eric.  The derivative of the Nehari functional. Annal. Acad. Scient. Fenn. 35 (2010) no 1, 291--307.

17. Radnell, David; and Schippers, Eric.  The  semigroup of rigged annuli and the Teichmueller space of the annulus. Journal of the London Mathematical Society 86 no 2 (2012), 321--342.

18. Penfound, Bryan; and Schippers, Eric.   Power matrices for Faber polynomials and conformal weldingComplex Variables and Elliptic Equations. 58 no 9 (2013) 1247--1259.

19.  Radnell, David; Schippers, Eric; and Staubach, Wulf.   Weil-Petersson class non-overlapping mappings into a Riemann surface.   Commun. Contemp. Math. 18, 1550060 (2016) [21 pages] DOI: http://dx.doi.org/10.1142/S0219199715500601

20. Radnell, David; Schippers, Eric; and Staubach, Wulf.   A Hilbert manifold structured on the Weil-Petersson class Teichmueller space of bordered Riemann surfaces.  with D. Radnell and W. Staubach.  Commun. Contemp. Math. 17, 1550016 (2015) [42 pages] DOI: http://dx.doi.org/10.1142/S0219199715500169

20 1/2. Radnell, David; Schippers, Eric; and Staubach, Wulf.   A Hilbert manifold structure on the refined Teichmueller space of bordered Riemann surfaces, arXiv:1207.0973. (This paper was submitted in two parts above as 20 and 21.  The notation in 20 and 21 has been updated to reflect the results in 24 and 25 below). 

21. Schippers, Eric; and Staubach, Wulf.   A symplectic functional analytic proof of the conformal welding theorem.   Proc. Amer. Math. Soc. 143 (2015), no. 1, 265–278.

22.  Radnell, David; Schippers, Eric; and Staubach, Wulf.  Dirichlet space of multiply-connected domains with Weil-Petersson class boundaries.   arxiv:1309.4337.   (Remark: never published.  More general results obtained and published in  "Dirichlet spaces of domains bounded by quasicrcles" below.)  

23. Radnell, David; Schippers, Eric; and Staubach, Wulf.   Quasiconformal maps of bordered Riemann surfaces with L^2 Beltrami differentials.   Jounal d'Analyse Mathematique 132 (1) (June 2017) 229--245.  Note: first posted in 2014, see 24 1/2 below.  

24. Radnell, David; Schippers, Eric; and Staubach, Wulf.  Convergence of the Weil-Petersson metric on the Teichmueller space of bordered Riemann surfacesCommunications in Contemporary Mathematics. 19 (1), (2017).  http://dx.doi.org/10.1142/S0219199716500255    Note: first posted on arxiv in 2014, see below..

24 1/2. Radnell, David; Schippers, Eric; and Staubach, Wulf.  A convergent Weil-Petersson metric on the Teichmueller space of bordered Riemann surfaces.   arXiv:1403.0868 (March 2014) (This arxiv paper contains the union of  the material in  publications 24 and 25.) 

25.  Remer, Krista; and Schippers, Eric.  Faber-Tietz functions and Grunsky coefficients for maps into a torus.  Complex Analysis and Operator Theory.  9 (2015) no. 8, 1663--1679.  

26.  Radnell, David; Schippers, Eric; and Staubach, Wulf.   Dirichlet problem and Sokhotski-Plemelj jump formula on Weil-Petersson class quasidisks.  with D. Radnell and W. Staubach.  Annales Academiae Scientiarum Fennicae.    41 (2016), 1--9.

27.  Schippers, Eric.  Conformal invariants associated with quadratic differentials.  arXiv:1608.00790.   
Israel J. Math. 223 (2018) no. 1, 449–491.  Springer SharedIt link.

28.  Radnell, David; Schippers, Eric; and Staubach, Wulf.  Quasiconformal Teichmuller theory as an analytic foundation for two-dimensional conformal field theory. 
 arXiv: 1605.004499v1  In `Lie algebras, Vertex Operator Algebras and Related Topics'. eds Katrina Barron, Elizabeth Jurisich, Antun Milas, Kailash Misra.  Contemporary Mathematics 695, Amer. Math. Soc. (2017).

29.  Schippers, Eric; and Staubach, Wulf.  Well-posedness of a Riemann-Hilbert problem on d-regular quasidisks.  Annales Academiae Scientiarum Fennicae.  42 (2017), 141--147.

30.  Schippers, Eric; and Staubach, Wulf.  Comparison moduli spaces.  with W. Staubach.  Chapter in: 
Complex analysis and dynamical systems, 231–271, Trends Math., Birkhäuser/Springer, Cham, 2018. arXiv:1706.09168v2

31.  Schippers, Eric.  Quadratic differentials and conformal invariants.   http://link.springer.com/article/10.1007/s41478-016-0014-5 The Journal of Analysis 24 (2)  (2016) 209--228.  DOI 10.1007/s41478-016-0014-5   Springer SharedIt link:  http://rdcu.be/pRuv
 
32.   Schippers, Eric; and Staubach, Wulf.  Harmonic reflection in quasicircles and well-posedness of a Riemann-Hilbert problem on quasidisks.   arXiv:1604.08453v3   Journal of Mathematical Analysis and Applications.  448 (2) 864--884, (2017).  

33.  Schippers, Eric; and Staubach, Wulf.
Riemann boundary value problem on quasidisks, Faber isomorphism and Grunsky operator.  Complex Anal. Oper. Theory 12 (2018), no. 2, 325–354.

34.  Radnell, David; Schippers, Eric; and Staubach, Wulf.  Dirichlet spaces of domains bounded by quasicrcles.  To appear in Communications in Contermporary Mathematics..  
arXiv:1705.01279v1.

35.  Radnell, David; Schippers, Eric; and Staubach, Wulf.  A Model of the Teichmueller space of genus-zero bordered surfaces by period maps.  
Conformal Geometry and. Dynamics 23 (2019), 32-51 arXiv:1710.06960
https://www.ams.org/journals/ecgd/2019-23-03/S1088-4173-2019-00332-1/

36.  Schippers, Eric; and Staubach, Wulf.  Transmission of harmonic functions through quasicircles on compact Riemann surfaces Annales Academiae Scientiarum Fennicae,
Volumen 45, 2020, 1111–1134 arXiv:1810.02147v2.

37.  Schippers, Eric; and Staubach, Wulf.  Plemelj-Sokhotski isomorphism  for quasicircles in Riemann surfaces and the Schiffer operators
Mathematische Annalen  378 (2020), 16131653  https://doi.org/10.1007/s00208-019-01922-4  https://link.springer.com/article/10.1007/s00208-019-01922-4

38.  Radnell, David; Schippers, Eric; Shirazi, Mohammad; and Staubach, Wulf.   Schiffer operators and computation of a determinant line in conformal field theory.  To appear in New York Journal of Mathematics.

39. Schippers, Eric; Shirazi, Mohammad; and Staubach, Wulf.  Schiffer operators and approximations on Riemann surfaces bordered by quasicircles. Journal of Geometric Analysis.   https://link.springer.com/article/10.1007/s12220-020-00508-w
arXiv:1911.03647

40. Schippers, Eric; Staubach, Wulf. Analysis on quasidisks: a unified approach through transmission and jump problems. Submitted.  https://arxiv.org/abs/2009.01954 

Selected Slides


The Weil-Petersson metric on a Teichmuller space of bordered surfaces.  AMS Special Session on Complex Function Theory and Special Functions, Lubbock, TX, April 2014.  

Conformal welding and the sewing equations.  Rutgers University Lie Groups/Quantum Mathematics Seminar.  Piscataway, NJ.  April 2014.  

Some analytic problems in conformal field theory.  MSRI Workshop on Infinite Dimensional Geometry. Berkeley, CA.  December 2013.

A correspondence between conformal field theory and Teichmuller theory.  McGill Analysis Seminar.  Montreal, QC.  February 2013.  

A functional-analytic proof of the conformal welding theorem.  CMS Winter Meeting, Ottawa December 2012. 

The Neretin-Segal semigroup and Teichmueller space of an annulus.  Second Bavaria-Quebec Meeting, Wuerzburg, Germany, November 2010.

The derivative of the Nehari functional.   AMS Special Session on Contemporary Complex and Special Function Theory,
Baylor University, Waco, TX.October 2009.  

The Loewner and Hadamard variations.  CMFT 2009, Bilkent University, Ankara, Turkey, June 2009.