Geometric function theory in one and several variables; planar harmonic mappings; differential geometry of curves; real and complex oscillation theory
Dean Faculty of Mathematics
Chair Department of Mathematics
Director Graduate Program
Professor
Associate Professor
Assistant Professor
Instructor
Thesis under professor B. Osgood, The Schwarzian derivative in Riemannian geometry, univalence criteria and quasiconformal reflections
Thesis under professor J. Gevirtz, The mean value theorem for quasi-isometries in Banach Spaces
Ignacio Tejeda, On the uniqueness of Ahlfors' Schwarzian in R, Undergraduate Thesis, 2017
Álvaro Ferrada, Affine and linear invariant families of harmonic mappings, Ph.D. 2015
Rodrigo Vargas, Convex mappings and Aleksandrov's measures, Ph.D. 2015
Willy Sierra, John domains on minimal surfaces, Ph.D. 2010
Rodrigo Vargas, Distortion theorems for Nehari's p-criterion, M.S. 2008
Paulina Barriga, Hilbert's metric on convex domains, M.S. 2006
Rodrigo Hernández, The Schwarzian derivative in several complex variables, Ph.D. 2004
Pilar Herreros, Hiperbolic convexity and the theorem of Gehring-Pommerenke, M.S. 2003
Fondecyt Grant 1190830, Applications of the Schwarzian derivative to curves and surfaces, P.I.
Fondecyt Grant 1150115, Harmonic and quasiconformal mappings, P.I.
Fondecyt Grant 1110321, Extensions of harmonic mappings, P.I.
Fondecyt Grant 1071019, The Schwarzian derivative, Weierstrass-Ennper lifts and harmonic mappings, P.I.
Fondecyt Grant 1030589, The Schwarzian derivative for harmonic mappings, P.I.
Fondecyt Grant 1030589, The Schwarzian derivative for harmonic mappings, P.I.
Fondecyt Grant 7030032 for International Cooperation, The Schwarzian derivative for harmonic mappings, P.I.
Fondecyt Grant 1000627, A variational method to study optimal univalence criteria, P.I.
Fondecyt Grant 7000627 for International Cooperation, A variational method to study optimal univalence criteria, P.I.
Fondecyt Grant 1971055, Convexity in geometric function theory and univalence criteria, P.I.
Fondecyt Grant 1940690, Applications of the Schwarzian derivative in analysis and geometry, P.I.
NSF Grant DM 590-01957, Associate Researcher
NSF Grant DM 590-01957, Associate Researcher
Schwarzian norms and two-point distortion, Pacific. J. Math. 254 (2011), 101-116 (with P. Duren, W. Ma, D. Mejía, D. Minda and B. Osgood)
Possible intervals for T- and M-orders of solutions of linear differential equations in the unit disc, Abstract and Applied Analysis 2011 (2011), article ID 928194, 25 pages (with J. Gröhn, J. Heittokangas and J. Rättyä)
On a theorem of Haimo regarding concave mappings, Annales Universitatis MariaeCurie-Sklodowska 65 (2011), 17-28 (with P. Duren and B. Osgood)
Schwarzian derivatives of convex mappings, Ann. Acad. Sci. Fenn. Math. 36 (2011),449-460 (with P. Duren and B. Osgood)
Generalized Schwarzian derivatives and higher order differential equations, Math. Proc. Cambridge Phil. Soc. 151 (2011), 339-354 (with J. Gröhn and J. Rättyä)
Injectivity criteria for holomorphic curves in Cn, Pure and Applied Mathematics Quarterly 7 (2011), 223-251 (with P. Duren and B. Osgood)
Two-point distorion theorems for harmonic mappings, Illinois J. Math. 53 (2009), 1062-1075 (with P. Duren and B. Osgood)
A condition for univalence in the polydisk, Comput. Methods and Function Theory 9 (2009), 443-454 (with R. Herná:ndez)
Oscillation of solutions of linear differential equations, Bull. Australian Math. Soc. 79 (2009), 161-169 (with P. Duren, B. Osgood and D. Stowe)
Möbius parametrizations of curves in Rn, Archiv der Mathematik 92 (2009), 626-636
Schwarzian derivatives of analytic and harmonic functions, Complex and Harmonic Analysis, Proceedings of the International Conference, May 25-27, 2006, Aristotle University of Thessaloniki, Greece, DEStech Publications (2007), pp. 25-33 (with P. Duren and B. Osgood)
Univalent harmonic mappings and linearly connected domains, J. Math. Anal. Appl.332 (2007), 1189-1194 (with R. Hernández)
On Ahlfors’ Schwarzian derivative and knots, Pacific J. Math. 231 (2007), 51-62
Univalence criteria for lifts of harmonic mappings to minimal surfaces, J. Geometric Analysis 17 (2007), 49-74 (with P. Duren and B. Osgood)
A generalization of Nehari’s p-criterion for univalence, Complex Variables Elliptic Equ. 52 (2007), 225-233 (with B. Osgood)
Schwarzian derivative criteria for valence of analytic and harmonic mappings, Math. Proc. Cambridge Phil. Soc. 143 (2007), 1-15 (with P. Duren and B. Osgood).
Simple curves in Rn and Ahlfors’ Schwarzian derivative, Proc. Amer. Math. Soc. 132 (2004), 223-230 (with J. Gevirtz)
Curvature properties of planar harmonic mappings, Comput. Methods and Function Theory 4 (2004), 127-142 (with P. Duren and B. Osgood)
Uniqueness and boundary behaviour of large solutions to elliptic problems with singular weights, Comm. Pure Appl. Anal. 3 (2004), 653-662 (with C. Cortázar, M. Elgueta and J. García-Melián)
Quasidisks and the Noshiro-Warschawski criterion, Complex Variables Theory Appl. 48 (2003), 967-985 (with J. Gevirtz)
The Schwarzian derivative for harmonic mappings, J. Analyse Math. 91 (2003), 329-351 (with P. Duren and B. Osgood)
On an elliptic problem with boundary blow-up and a singular weight: the radial case, Proc. Royal Soc. Edinburgh 133 A (2003) , 1283-1297 (with C. Cortázar, M. Elgueta, C. Flores, J. García-Melián and R. Letelier)
Characteristic properties of Nehari functions, Pacific J. Math. 188 (1999), 83-94 (with Ch. Pommerenke)
On the integral means and Schwarzian derivative, Complex Variables Theory Appl. 39(1999), 177-189 (with Ch. Pommerenke)
Recent Progress on the Geometry of Univalence Criteria, Contemporary Math. 240 (1999), 75-87 (with B. Osgood)
On the coefficients of small univalent functions, Results in Math. 33 (1998), 79-86 (with Ch. Pommerenke and B. Osgood)
General univalence criteria in the unit disc: extensions and extremal functions, Ann. Acad. Sci. Fenn. Math. 23 (1998), 101-132 (with B. Osgood)
John domains and a univalence criterion of Ahlfors, Results in Math. 33 (1998), 203-207 (with B. Osgood)
Finding complete conformal metrics to extend conformal mappings, Indiana U. Math. J. 47 (1998), 1273-1291 (with B. Osgood)
A unified approach to univalence criteria in the unit disc, Proc. Amer. Math. Soc. 123 (1995), 441-453
Applications of subordination chains to starlike mappings in Cn, Pacific J. Math. 168 (1995), 33-48
An extension of a theorem of Gehring and Pommerenke, Israel J. Math. 91 (1995),393-407 (with B. Osgood)
Jhonattan Gaona, Iason Efraimidis, Rodrigo Hernandez, Martin Chuaqui, Alvaro Ferrada, Rodrigo Vargas, Hugo Arbeláez, Willy Sierra